View source for Shoelace formula for polygonal area

{{task}}
Given the <code>n + 1</code> vertices <code>x[0], y[0] .. x[N], y[N]</code> of a simple polygon described in a clockwise direction, then the polygon's area can be calculated by:
<pre>
abs( (sum(x[0]*y[1] + ... x[n-1]*y[n]) + x[N]*y[0]) -
     (sum(x[1]*y[0] + ... x[n]*y[n-1]) + x[0]*y[N])
   ) / 2</pre>
(Where <code>abs</code> returns the absolute value)

;Task:
Write a function/method/routine to use the the [[wp:Shoelace formula|Shoelace formula]] to calculate the area of the polygon described by the ordered points:
     <big> (3,4), (5,11), (12,8), (9,5), and (5,6) </big>


Show the answer here, on this page.
<br><br>

=={{header|11l}}==
{{trans|Python}}

<syntaxhighlight lang="11l">F area_by_shoelace(x, y)
   R abs(sum(zip(x, y[1..] [+] y[0.<1]).map((i, j) -> i * j))
        -sum(zip(x[1..] [+] x[0.<1], y).map((i, j) -> i * j))) / 2

V points = [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)]
V x = points.map(p -> p[0])
V y = points.map(p -> p[1])

print(area_by_shoelace(x, y))</syntaxhighlight>

{{out}}
<pre>
30
</pre>

=={{header|360 Assembly}}==
<syntaxhighlight lang="360asm">*        SHOELACE                  25/02/2019
SHOELACE CSECT
         USING  SHOELACE,R15       base register
         MVC    SUPS(8),POINTS     x(nt+1)=x(1); y(nt+1)=y(1)
         LA     R9,0               area=0
         LA     R7,POINTS          @x(1)
         LA     R6,NT              do i=1 to nt
LOOP     L      R3,0(R7)             x(i)
         M      R2,12(R7)            *y(i+1)
         L      R5,8(R7)             x(i+1)
         M      R4,4(R7)             *y(i)
         SR     R3,R5                x(i)*y(i+1)-x(i+1)*y(i)
         AR     R9,R3                area=area+x(i)*y(i+1)-x(i+1)*y(i)
         LA     R7,8(R7)             @x(i++)
         BCT    R6,LOOP            enddo
         LPR    R9,R9              area=abs(area)
         SRA    R9,1               area=area/2
         XDECO  R9,PG              edit area
         XPRNT  PG,L'PG            print area
         BR     R14                return to caller
NT       EQU    (SUPS-POINTS)/8    nt  number of points
POINTS   DC     F'3',F'4',F'5',F'11',F'12',F'8',F'9',F'5',F'5',F'6'
SUPS     DS     2F                 x(nt+1),y(nt+1)
PG       DC     CL12' '            buffer
         REGEQU
         END    SHOELACE</syntaxhighlight>
{{out}}
<pre>
          30
</pre>

=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
{{libheader|Action! Real Math}}
<syntaxhighlight lang="action!">INCLUDE "H6:REALMATH.ACT"

PROC Area(INT ARRAY xs,ys BYTE count REAL POINTER res)
  BYTE i,next
  REAL x1,y1,x2,y2,tmp1,tmp2

  IntToReal(0,res)
  IntToReal(xs(0),x1) IntToReal(ys(0),y1)
  FOR i=0 TO count-1
  DO
    next=i+1
    IF next=count THEN
      next=0
    FI
    IntToReal(xs(next),x2) IntToReal(ys(next),y2)

    RealMult(x1,y2,tmp1)
    RealAdd(res,tmp1,tmp2)
    RealMult(x2,y1,tmp1)
    RealSub(tmp2,tmp1,res)

    RealAssign(x2,x1) RealAssign(y2,y1)
  OD
  
  RealAbs(res,tmp1)
  IntToReal(2,tmp2)
  RealDiv(tmp1,tmp2,res)
RETURN

PROC PrintPolygon(INT ARRAY xs,ys BYTE count)
  BYTE i

  FOR i=0 TO count-1
  DO
    PrintF("(%I,%I)",xs(i),ys(i))
    IF i<count-1 THEN
      Print(", ")
    ELSE
      PutE()
    FI
  OD
RETURN

PROC Test(INT ARRAY xs,ys BYTE count)
  REAL res

  Area(xs,ys,count,res)
  Print("Polygon: ")
  PrintPolygon(xs,ys,count)

  Print("Area: ")
  PrintRE(res) PutE()
RETURN

PROC Main()
  INT ARRAY
    xs(5)=[3 5 12 9 5],
    ys(5)=[4 11 8 5 6]

  Put(125) PutE() ;clear screen

  Test(xs,ys,5)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Shoelace_formula_for_polygonal_area.png Screenshot from Atari 8-bit computer]
<pre>
Polygon: (3,4), (5,11), (12,8), (9,5), (5,6)
Area: 30
</pre>

=={{header|Ada}}==
{{works with|Ada|Ada|83}}

<syntaxhighlight lang="ada">with Ada.Text_IO;

procedure Shoelace_Formula_For_Polygonal_Area
is
   type Point is record
      x, y : Float;
   end record;
   
   type Polygon is array (Positive range <>) of Point;
   
   function Shoelace(input : in Polygon) return Float
   is
      sum_1 : Float := 0.0;
      sum_2 : Float := 0.0;
      tmp : constant Polygon := input & input(input'First);
   begin
      for I in tmp'First .. tmp'Last - 1 loop
         sum_1 := sum_1 + tmp(I).x * tmp(I+1).y;
         sum_2 := sum_2 + tmp(I+1).x * tmp(I).y;
      end loop;
      return abs(sum_1 - sum_2) / 2.0;
   end Shoelace;
   
   my_polygon : constant Polygon :=
     ((3.0, 4.0),
      (5.0, 11.0),
      (12.0, 8.0),
      (9.0, 5.0),
      (5.0, 6.0));
begin
   Ada.Text_IO.Put_Line(Shoelace(my_polygon)'Img);
end Shoelace_Formula_For_Polygonal_Area;</syntaxhighlight>
{{out}}
<pre> 3.00000E+01
</pre>

=={{header|ALGOL 60}}==
Optimized version:
 '''begin'''
     '''comment''' Shoelace formula for polygonal area - Algol 60;
     '''real''' '''array''' x[1:33],y[1:33];
     '''integer''' i,n;
     '''real''' a;
     ininteger(0,n);
     '''for''' i:=1 '''step''' 1 '''until''' n '''do'''
     '''begin'''
         inreal(0,x[i]);
         inreal(0,y[i])
     '''end''';   
     x[i]:=x[1];
     y[i]:=y[1];
     a:=0;
     '''for''' i:=1 '''step''' 1 '''until''' n '''do'''
         a:=a+x[i]*y[i+1]-x[i+1]*y[i];   
     a:=abs(a/2.);
     outreal(1,a)
 '''end'''
{{out}}
<pre>
     30.00
</pre>
Non-optimized version:
 '''begin'''
     '''comment''' Shoelace formula for polygonal area - Algol 60;
     '''real''' '''array''' x[1:32],y[1:32]; 
     '''integer''' i,j,n;
     '''real''' a;
     ininteger(0,n);
     '''for''' i:=1 '''step''' 1 '''until''' n '''do'''
     '''begin'''
         inreal(0,x[i]); inreal(0,y[i])
     '''end''';   
     a:=0;
     '''for''' i:=1 '''step''' 1 '''until''' n '''do'''
     '''begin'''
         j:='''if''' i=n '''then''' 1 '''else''' i+1;
         a:=a+x[i]*y[j]-x[j]*y[i]
     '''end''';   
     a:=abs(a/2.);
     outreal(1,a)
 '''end'''
{{out}}
<pre>
     30.00
</pre>

=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">BEGIN
    # returns the area of the polygon defined by the points p using the Shoelace formula #
    OP  AREA = ( [,]REAL p )REAL:
        BEGIN
            [,]REAL points = p[ AT 1, AT 1 ]; # normalise array bounds to start at 1 #
            IF 2 UPB points /= 2 THEN
                # the points do not have 2 coordinates #
                -1
            ELSE
                REAL   result := 0;
                INT    n       = 1 UPB points;
                IF n > 1 THEN
                    # there at least two points #
                    []REAL x   = points[ :, 1 ];
                    []REAL y   = points[ :, 2 ];
                    FOR i TO 1 UPB points - 1 DO
                        result +:= x[ i     ] * y[ i + 1 ];
                        result -:= x[ i + 1 ] * y[ i     ]
                    OD;
                    result     +:= x[ n ] * y[ 1 ];
                    result     -:= x[ 1 ] * y[ n ]
                FI;
                ( ABS result ) / 2
            FI
        END # AREA # ;

    # test case as per the task #
    print( ( fixed( AREA [,]REAL( ( 3.0, 4.0 ), ( 5.0, 11.0 ), ( 12.0, 8.0 ), ( 9.0, 5.0 ), ( 5.0, 6.0 ) ), -6, 2 ), newline ) )
END
</syntaxhighlight>
{{out}}
<pre>
 30.00
</pre>

=={{header|APL}}==
{{works with|Dyalog APL}}
<syntaxhighlight lang="apl">shoelace ← 2÷⍨|∘(((1⊃¨⊢)+.×1⌽2⊃¨⊢)-(1⌽1⊃¨⊢)+.×2⊃¨⊢)</syntaxhighlight>
{{out}}
<pre>      shoelace (3 4) (5 11) (12 8) (9 5) (5 6)
30</pre>

=={{header|Arturo}}==
<syntaxhighlight lang="arturo">define :point [x,y][]

shoelace: function [pts][
    [leftSum, rightSum]: 0

    loop 0..dec size pts 'i [
        j: (i + 1) % size pts
        'leftSum + pts\[i]\x * pts\[j]\y
        'rightSum + pts\[j]\x * pts\[i]\y
    ]
    return 0.5 * abs leftSum - rightSum
]

points: @[
    to :point [3.0, 4.0]
    to :point [5.0, 11.0]
    to :point [12.0, 8.0]
    to :point [9.0, 5.0]
    to :point [5.0, 6.0]
]

print shoelace points</syntaxhighlight>

{{out}}

<pre>30.0</pre>

=={{header|AutoHotkey}}==
<syntaxhighlight lang="autohotkey">V := [[3, 4], [5, 11], [12, 8], [9, 5], [5, 6]]

n := V.Count()
for i, O in V
    Sum += V[i, 1] * V[i+1, 2]  -  V[i+1, 1] * V[i, 2]
MsgBox % result := Abs(Sum += V[n, 1] * V[1, 2]  -  V[1, 1] * V[n, 2]) / 2</syntaxhighlight>
{{out}}
<pre>30.000000</pre>

=={{header|BASIC256}}==
<syntaxhighlight lang="basic256">arraybase 1
dim array = {{3,4}, {5,11}, {12,8}, {9,5}, {5,6}}

print "The area of the polygon = "; Shoelace(array)
end

function Shoelace(p)
    sum = 0
    for i = 1 to p[?][] -1
        sum += p[i][1] * p[i +1][2]
        sum -= p[i +1][1] * p[i][2]
    next i
    sum += p[i][1] * p[1][2]
    sum -= p[1][1] * p[i][2]
    return abs(sum) \ 2
end function</syntaxhighlight>

=={{header|C}}==
Reads the points from a file whose name is supplied via the command line, prints out usage if invoked incorrectly. 
<syntaxhighlight lang="c">
#include<stdlib.h>
#include<stdio.h>
#include<math.h>

typedef struct{
	double x,y;
}point;

double shoelace(char* inputFile){
	int i,numPoints;
	double leftSum = 0,rightSum = 0;
	
	point* pointSet;
	FILE* fp = fopen(inputFile,"r");
	
	fscanf(fp,"%d",&numPoints);
	
	pointSet = (point*)malloc((numPoints + 1)*sizeof(point));
	
	for(i=0;i<numPoints;i++){
		fscanf(fp,"%lf %lf",&pointSet[i].x,&pointSet[i].y);
	}
	
	fclose(fp);
	
	pointSet[numPoints] = pointSet[0];
	
	for(i=0;i<numPoints;i++){
		leftSum += pointSet[i].x*pointSet[i+1].y;
		rightSum += pointSet[i+1].x*pointSet[i].y;
	}
	
	free(pointSet);
	
	return 0.5*fabs(leftSum - rightSum);
}

int main(int argC,char* argV[])
{
	if(argC==1)
		printf("\nUsage : %s <full path of polygon vertices file>",argV[0]);
	
	else
		printf("The polygon area is %lf square units.",shoelace(argV[1]));
	
	return 0;
}
</syntaxhighlight>
Input file, first line specifies number of points followed by the ordered vertices set with one vertex on each line.
<pre>
5
3 4
5 11
12 8
9 5
5 6
</pre>
Invocation and output :
<pre>
C:\rosettaCode>shoelace.exe polyData.txt
The polygon area is 30.000000 square units.
</pre>

=={{header|C sharp|C#}}==
{{trans|Java}}
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;

namespace ShoelaceFormula {
    using Point = Tuple<double, double>;

    class Program {
        static double ShoelaceArea(List<Point> v) {
            int n = v.Count;
            double a = 0.0;
            for (int i = 0; i < n - 1; i++) {
                a += v[i].Item1 * v[i + 1].Item2 - v[i + 1].Item1 * v[i].Item2;
            }
            return Math.Abs(a + v[n - 1].Item1 * v[0].Item2 - v[0].Item1 * v[n - 1].Item2) / 2.0;
        }

        static void Main(string[] args) {
            List<Point> v = new List<Point>() {
                new Point(3,4),
                new Point(5,11),
                new Point(12,8),
                new Point(9,5),
                new Point(5,6),
            };
            double area = ShoelaceArea(v);
            Console.WriteLine("Given a polygon with vertices [{0}],", string.Join(", ", v));
            Console.WriteLine("its area is {0}.", area);
        }
    }
}</syntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
its area is 30.</pre>

=={{header|C++}}==
{{trans|D}}
<syntaxhighlight lang="cpp">#include <iostream>
#include <tuple>
#include <vector>

using namespace std;

double shoelace(vector<pair<double, double>> points) {
	double leftSum = 0.0;
	double rightSum = 0.0;

	for (int i = 0; i < points.size(); ++i) {
		int j = (i + 1) % points.size();
		leftSum  += points[i].first * points[j].second;
		rightSum += points[j].first * points[i].second;
	}

	return 0.5 * abs(leftSum - rightSum);
}

void main() {
	vector<pair<double, double>> points = {
		make_pair( 3,  4),
		make_pair( 5, 11),
		make_pair(12,  8),
		make_pair( 9,  5),
		make_pair( 5,  6),
	};

	auto ans = shoelace(points);
	cout << ans << endl;
}</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|Cowgol}}==
<syntaxhighlight lang="cowgol">include "cowgol.coh";

typedef Coord is uint16; # floating point types are not supported

record Point is
    x: Coord;
    y: Coord;
end record;

sub shoelace(p: [Point], length: intptr): (area: Coord) is
    var left: Coord := 0;
    var right: Coord := 0;
    
    var y0 := p.y;
    var x0 := p.x;
    
    while length > 1 loop
        var xp := p.x;
        var yp := p.y;
        p := @next p;
        left := left + xp * p.y;
        right := right + yp * p.x;
        length := length - 1;
    end loop;
    
    left := left + y0 * p.x;
    right := right + x0 * p.y;
    if left < right then
        area := right - left;
    else
        area := left - right;
    end if;
    
    area := area / 2;
end sub;

var polygon: Point[] := {{3,4},{5,11},{12,8},{9,5},{5,6}};
print_i16(shoelace(&polygon[0], @sizeof polygon));
print_nl();</syntaxhighlight>
{{out}}
<pre>30</pre>
=={{header|D}}==
<syntaxhighlight lang="d">import std.stdio;

Point[] pnts = [{3,4}, {5,11}, {12,8}, {9,5}, {5,6}];

void main() {
    auto ans = shoelace(pnts);
    writeln(ans);
}

struct Point {
    real x, y;
}

real shoelace(Point[] pnts) {
    real leftSum = 0, rightSum = 0;

    for (int i=0; i<pnts.length; ++i) {
        int j = (i+1) % pnts.length;
        leftSum  += pnts[i].x * pnts[j].y;
        rightSum += pnts[j].x * pnts[i].y;
    }

    import std.math : abs;
    return 0.5 * abs(leftSum - rightSum);
}

unittest {
    auto ans = shoelace(pnts);
    assert(ans == 30);
}</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
In keeping with the principles of modularity and reusability, the problem has been broken down into subroutines that can process any polygon. In other words, the subroutines don't just solve the area of one polygon; they can find the area of any polygon.

<syntaxhighlight lang="Delphi">
{Create a 2D vector type}

type T2DVector = record
 X, Y: double;
 end;

{Test polygon}

var Polygon: array [0..4] of T2DVector =
 ((X:3; Y:4), (X:5; Y:11), (X:12; Y:8), (X:9; Y:5), (X:5; Y:6));


function GetPolygonArea(Polygon: array of T2DVector): double;
{Return the area of the polygon }
{K = [(x1y2 + x2y3 + x3y4 + ... + xny1) - (x2y1 + x3y2 + x4y3 + ... + x1yn)]/2}
var I,Inx: integer;
var P1,P2: T2DVector;
var Sum1,Sum2: double;
begin
Result:=0;
Sum1:=0; Sum2:=0;
for I:=0 to Length(Polygon)-1 do
	begin
	{Vector back to the beginning}
	if I=(Length(Polygon)-1) then Inx:=0
	else Inx:=I+1;
	P1:=Polygon[I];
	P2:=Polygon[Inx];
	Sum1:=Sum1 + P1.X * P2.Y;
	Sum2:=Sum2 + P2.X * P1.Y;
	end;
Result:=abs((Sum1 - Sum2)/2);
end;

procedure ShowPolygon(Poly: array of T2DVector; Memo: TMemo);
var I: integer;
var S: string;
begin
S:='';
for I:=0 to High(Poly) do
 S:=S+Format('(%2.1F, %2.1F) ',[Poly[I].X, Poly[I].Y]);
Memo.Lines.Add(S);
end;


procedure ShowPolygonArea(Memo: TMemo);
var Area: double;
begin
ShowPolygon(Polygon,Memo);
Area:=GetPolygonArea(Polygon);
Memo.Lines.Add('Area: '+FloatToStrF(Area,ffFixed,18,2));
end;


</syntaxhighlight>
{{out}}
<pre>
(3.0, 4.0) (5.0, 11.0) (12.0, 8.0) (9.0, 5.0) (5.0, 6.0) 
Area: 30.00
Elapsed Time: 3.356 ms.
</pre>


=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
proc shoelace . p[][] res .
   sum = 0
   for i = 1 to len p[][] - 1
      sum += p[i][1] * p[i + 1][2]
      sum -= p[i + 1][1] * p[i][2]
   .
   sum += p[i][1] * p[1][2]
   sum -= p[1][1] * p[i][2]
   res = abs sum / 2
.
data[][] = [ [ 3 4 ] [ 5 11 ] [ 12 8 ] [ 9 5 ] [ 5 6 ] ]
shoelace data[][] res
print res
</syntaxhighlight>

=={{header|Elixir}}==
<syntaxhighlight lang="elixir">
def shoelace(points) do
  points
  |> Enum.reduce({0, List.last(points)}, fn {x1, y1}, {sum, {x0, y0}} ->
    {sum + (y0 * x1 - x0 * y1), {x1, y1}}
  end)
  |> elem(0)
  |> div(2)
end
</syntaxhighlight>

=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Shoelace formula for area of polygon. Nigel Galloway: April 11th., 2018
let fN(n::g) = abs(List.pairwise(n::g@[n])|>List.fold(fun n ((nα,gα),(nβ,gβ))->n+(nα*gβ)-(gα*nβ)) 0.0)/2.0
printfn "%f" (fN [(3.0,4.0); (5.0,11.0); (12.0,8.0); (9.0,5.0); (5.0,6.0)])</syntaxhighlight>
{{out}}
<pre>
30.000000
</pre>

=={{header|Factor}}==
By constructing a <code>circular</code> from a sequence, we can index elements beyond the length of the sequence, wrapping around to the beginning. We can also change the beginning of the sequence to an arbitrary index. This allows us to use <code>2map</code> to cleanly obtain a sum.
<syntaxhighlight lang="factor">USING: circular kernel math prettyprint sequences ;
IN: rosetta-code.shoelace

CONSTANT: input { { 3 4 } { 5 11 } { 12 8 } { 9 5 } { 5 6 } }

: align-pairs ( pairs-seq -- seq1 seq2 )
    <circular> dup clone [ 1 ] dip
    [ change-circular-start ] keep ;

: shoelace-sum ( seq1 seq2 -- n )
    [ [ first ] [ second ] bi* * ] 2map sum ;

: shoelace-area ( pairs-seq -- area )
    [ align-pairs ] [ align-pairs swap ] bi
    [ shoelace-sum ] 2bi@ - abs 2 / ;

input shoelace-area .</syntaxhighlight>
{{out}}
<pre>
30
</pre>

=={{header|Fortran}}==
===Fortran 90===
Except for the use of "END FUNCTION ''name'' instead of just END, and the convenient function SUM with array span expressions (so SUM(P) rather than a DO-loop to sum the elements of array P), both standardised with F90, this would be acceptable to F66, which introduced complex number arithmetic. Otherwise, separate X and Y arrays would be needed, but complex numbers seemed convenient seeing as (x,y) pairs are involved. But because the MODULE facility of F90 has not been used, routines invoking functions must declare the type of the function names, especially if the default types are unsuitable, as here. In function AREA, the x and y parts are dealt with together, but in AREASL they might be better as separate arrays, thus avoiding the DIMAG and DBLE functions to extract the x and y parts. Incidentally, the x and y parts can be interchanged and the calculation still works. Comparing the two resulting areas might give some indication of their accuracy.

If the MODULE protocol were used, the size of an array parameter is passed as a secret additional parameter accessible via the special function UBOUND, but otherwise it must be passed as an explicit parameter. A quirk of the compiler requires that N be declared before it appears in <code>DOUBLE COMPLEX P(N)</code> so as it is my practice to declare parameters in the order specified, here N comes before P. However, it is not clear whether specifying P(N) does much good (as in array index checking) as an alternative is to specify P(*) meaning merely that the array has one dimension, or even P(12345) to the same effect, with no attention to the actual numerical value. See for example [[Array_length#Fortran]] <syntaxhighlight lang="fortran">      DOUBLE PRECISION FUNCTION AREA(N,P)	!Calculates the area enclosed by the polygon P.
C   Uses the mid-point rule for integration. Consider the line joining (x1,y1) to (x2,y2)
C The area under that line (down to the x-axis) is the y-span midpoint (y1 + y2)/2 times the width (x2 - x1)
C This is the trapezoidal rule for a single interval, and follows from simple geometry.
C Now consider a sequence of such points heading in the +x direction: each successive interval's area is positive.
C Follow with a sequence of points heading in the -x direction, back to the first point: their areas are all negative.
C The resulting sum is the area below the +x sequence and above the -x sequence: the area of the polygon.
C   The point sequence can wobble as it wishes and can meet the other side, but it must not cross itself
c as would be done in a figure 8 drawn with a crossover instead of a meeting.
C   A clockwise traversal (as for an island) gives a positive area; use anti-clockwise for a lake.
       INTEGER N		!The number of points.
       DOUBLE COMPLEX P(N)	!The points.
       DOUBLE COMPLEX PP,PC	!Point Previous and Point Current.
       DOUBLE COMPLEX W		!Polygon centre. Map coordinates usually have large offsets.
       DOUBLE PRECISION A	!The area accumulator.
       INTEGER I		!A stepper.
        IF (N.LT.3) STOP "Area: at least three points are needed!"	!Good grief.
        W = (P(1) + P(N/3) + P(2*N/3))/3	!An initial working average.
        W = SUM(P(1:N) - W)/N + W	!A good working average is the average itself.
        A = 0			!The area enclosed by the point sequence.
        PC = P(N) - W		!The last point is implicitly joined to the first.
        DO I = 1,N		!Step through the positions.
          PP = PC			!Previous position.
          PC = P(I) - W			!Current position.
          A = (DIMAG(PC) + DIMAG(PP))*(DBLE(PC) - DBLE(PP)) + A	!Area integral component.
        END DO			!On to the next position.
        AREA = A/2		!Divide by two once.
      END FUNCTION AREA		!The units are those of the points.

      DOUBLE PRECISION FUNCTION AREASL(N,P)	!Area enclosed by polygon P, by the "shoelace" method.
       INTEGER N		!The number of points.
       DOUBLE COMPLEX P(N)	!The points.
       DOUBLE PRECISION A	!A scratchpad.
        A = SUM(DBLE(P(1:N - 1)*DIMAG(P(2:N)))) + DBLE(P(N))*DIMAG(P(1))
     1    - SUM(DBLE(P(2:N)*DIMAG(P(1:N - 1)))) - DBLE(P(1))*DIMAG(P(N))
        AREASL = A/2		!The midpoint formula requires a halving.
      END FUNCTION AREASL	!Negative for clockwise, positive for anti-clockwise.

      INTEGER ENUFF
      DOUBLE PRECISION AREA,AREASL	!The default types are not correct.
      DOUBLE PRECISION A1,A2		!Scratchpads, in case of a debugging WRITE within the functions.
      PARAMETER (ENUFF = 5)		!The specification.
      DOUBLE COMPLEX POINT(ENUFF)	!Could use X and Y arrays instead.
      DATA POINT/(3D0,4D0),(5D0,11D0),(12D0,8D0),(9D0,5D0),(5D0,6D0)/	!"D" for double precision.

      WRITE (6,*) POINT
      A1 = AREA(5,POINT)
      A2 = AREASL(5,POINT)
      WRITE (6,*) "A=",A1,A2
      END</syntaxhighlight>

Output: WRITE (6,*) means write to output unit six (standard output) with free-format (the *). Note the different sign convention.
<pre>
 (3.00000000000000,4.00000000000000) (5.00000000000000,11.0000000000000)
 (12.0000000000000,8.00000000000000) (9.00000000000000,5.00000000000000)
 (5.00000000000000,6.00000000000000)
 A=   30.0000000000000       -30.0000000000000
</pre>

The "shoelace" method came as a surprise to me, as I've always used what I had thought the "obvious" method. Note that function AREA makes one pass through the point data not two, and because map coordinate values often have large offsets a working average is used to reduce the loss of precision. This requires faith that <code>SUM(P(1:N) - W)</code> will be evaluated as written, not as <code>SUM(P(1:N)) - N*W</code> with even greater optimisation opportunity awaiting in cancelling further components of the expression. For example, the New Zealand metric grid has (2510000,6023150) as (Easting,Northing) or (x,y) at its central point of 41°S 173°E rather than (0,0) so seven digits of precision are used up. If anyone wants a copy of a set of point sequences for NZ (30,000 positions, 570KB) with lots of islands and lakes, even a pond in an island in a lake in the North Island...

===Fortran I===
In orginal FORTRAN 1957: 
<syntaxhighlight lang="fortran">
C SHOELACE FORMULA FOR POLYGONAL AREA
      DIMENSION X(33),Y(33)
      READ 101,N
      DO 1 I=1,N
   1    READ 102,X(I),Y(I)   
      X(I)=X(1)
      Y(I)=Y(1)
      A=0
      DO 2 I=1,N
   2    A=A+X(I)*Y(I+1)-X(I+1)*Y(I)
      A=ABSF(A/2.)
      PRINT 303,A
      STOP
 101  FORMAT(I2)
 102  FORMAT(2F6.2)
 303  FORMAT(F10.2)

</syntaxhighlight>
{{in}}
<pre>
 5
  3.00  4.00 
  5.00 11.00
 12.00  8.00
  9.00  5.00
  5.00  6.00
</pre>
{{out}}
<pre>
     30.00
</pre>

=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">' version 18-08-2017
' compile with: fbc -s console

Type _point_
    As Double x, y
End Type

Function shoelace_formula(p() As _point_ ) As Double

    Dim As UInteger i
    Dim As Double sum

    For i = 1 To UBound(p) -1
        sum += p(i   ).x * p(i +1).y
        sum -= p(i +1).x * p(i   ).y
    Next
    sum += p(i).x * p(1).y
    sum -= p(1).x * p(i).y

    Return Abs(sum) / 2
End Function

' ------=< MAIN >=------

Dim As _point_ p_array(1 To ...) = {(3,4), (5,11), (12,8), (9,5), (5,6)}

Print "The area of the polygon ="; shoelace_formula(p_array())

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre>The area of the polygon = 30</pre>

=={{header|Fōrmulæ}}==

{{FormulaeEntry|page=https://formulae.org/?script=examples/Shoelace_formula_for_polygonal_area}}

'''Solution'''

[[File:Fōrmulæ - Shoelace formula 01.png]]

'''Test case'''

[[File:Fōrmulæ - Shoelace formula 02.png]]

[[File:Fōrmulæ - Shoelace formula 03.png]]

=={{header|Go}}==
<syntaxhighlight lang="go">package main

import "fmt"

type point struct{ x, y float64 }

func shoelace(pts []point) float64 {
    sum := 0.
    p0 := pts[len(pts)-1]
    for _, p1 := range pts {
        sum += p0.y*p1.x - p0.x*p1.y
        p0 = p1
    }
    return sum / 2
}

func main() {
    fmt.Println(shoelace([]point{{3, 4}, {5, 11}, {12, 8}, {9, 5}, {5, 6}}))
}</syntaxhighlight>
{{out}}
<pre>
30
</pre>

=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Data.Bifunctor (bimap)

----------- SHOELACE FORMULA FOR POLYGONAL AREA ----------

-- The area of a polygon formed by
-- the list of (x, y) coordinates.

shoelace :: [(Double, Double)] -> Double
shoelace =
  let calcSums ((x, y), (a, b)) = bimap (x * b +) (a * y +)
   in (/ 2)
        . abs
        . uncurry (-)
        . foldr calcSums (0, 0)
        . (<*>) zip (tail . cycle)

--------------------------- TEST -------------------------
main :: IO ()
main =
  print $
    shoelace [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)]</syntaxhighlight>
{{out}}
<pre>30.0</pre>

=={{header|J}}==

Implementation:

<syntaxhighlight lang="j">shoelace=:verb define
  0.5*|+/((* 1&|.)/ - (* _1&|.)/)|:y
)</syntaxhighlight>

Task example:

<syntaxhighlight lang="j">   shoelace 3 4,5 11,12 8,9 5,:5 6
30</syntaxhighlight>

Exposition:

We start with our list of coordinate pairs

<syntaxhighlight lang="j">   3 4,5 11,12 8,9 5,:5 6
 3  4
 5 11
12  8
 9  5
 5  6</syntaxhighlight>

But the first thing we do is transpose them so that x coordinates and y coordinates are the two items we are working with:

<syntaxhighlight lang="j">   |:3 4,5 11,12 8,9 5,:5 6
3  5 12 9 5
4 11  8 5 6</syntaxhighlight>

We want to rotate the y list by one (in each direction) and multiply the x list items by the corresponding y list items. Something like this, for example:

<syntaxhighlight lang="j">   3 5 12 9 5* 1|.4 11 8 5 6
33 40 60 54 20</syntaxhighlight>

Or, rephrased:

<syntaxhighlight lang="j">   (* 1&|.)/|:3 4,5 11,12 8,9 5,:5 6
33 40 60 54 20</syntaxhighlight>

We'll be subtracting what we get when we rotate in the other direction, which looks like this:

<syntaxhighlight lang="j">   ((* 1&|.)/ - (* _1&|.)/)|:3 4,5 11,12 8,9 5,:5 6
15 20 _72 _18 _5</syntaxhighlight>

Finally, we add up that list, take the absolute value (there are contexts where signed area is interesting - for example, some graphics application - but that was not a part of this task) and divide that by 2.

=={{header|Java}}==
{{trans|Kotlin}}
{{works with|Java|9}}
<syntaxhighlight lang="java">import java.util.List;

public class ShoelaceFormula {
    private static class Point {
        int x, y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return String.format("(%d, %d)", x, y);
        }
    }

    private static double shoelaceArea(List<Point> v) {
        int n = v.size();
        double a = 0.0;
        for (int i = 0; i < n - 1; i++) {
            a += v.get(i).x * v.get(i + 1).y - v.get(i + 1).x * v.get(i).y;
        }
        return Math.abs(a + v.get(n - 1).x * v.get(0).y - v.get(0).x * v.get(n - 1).y) / 2.0;
    }

    public static void main(String[] args) {
        List<Point> v = List.of(
            new Point(3, 4),
            new Point(5, 11),
            new Point(12, 8),
            new Point(9, 5),
            new Point(5, 6)
        );
        double area = shoelaceArea(v);
        System.out.printf("Given a polygon with vertices %s,%n", v);
        System.out.printf("its area is %f,%n", area);
    }
}</syntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
its area is 30.000000,</pre>

=={{header|JavaScript}}==
<syntaxhighlight lang="javascript">(() => {
    "use strict";

    // ------- SHOELACE FORMULA FOR POLYGONAL AREA -------

    // shoelaceArea :: [(Float, Float)] -> Float
    const shoeLaceArea = vertices => abs(
        uncurry(subtract)(
            ap(zip)(compose(tail, cycle))(
                vertices
            )
            .reduce(
                (a, x) => [0, 1].map(b => {
                    const n = Number(b);

                    return a[n] + (
                        x[0][n] * x[1][Number(!b)]
                    );
                }),
                [0, 0]
            )
        )
    ) / 2;


    // ----------------------- TEST -----------------------
    const main = () => {
        const ps = [
            [3, 4],
            [5, 11],
            [12, 8],
            [9, 5],
            [5, 6]
        ];

        return [
                "Polygonal area by shoelace formula:",
                `${JSON.stringify(ps)} -> ${shoeLaceArea(ps)}`
            ]
            .join("\n");
    };


    // ---------------- GENERIC FUNCTIONS -----------------

    // abs :: Num -> Num
    const abs = x =>
        // Absolute value of a given number
        // without the sign.
        0 > x ? -x : x;


    // ap :: (a -> b -> c) -> (a -> b) -> (a -> c)
    const ap = f =>
        // Applicative instance for functions.
        // f(x) applied to g(x).
        g => x => f(x)(
            g(x)
        );


    // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
    const compose = (...fs) =>
        // A function defined by the right-to-left
        // composition of all the functions in fs.
        fs.reduce(
            (f, g) => x => f(g(x)),
            x => x
        );


    // cycle :: [a] -> Generator [a]
    const cycle = function* (xs) {
        // An infinite repetition of xs,
        // from which an arbitrary prefix
        // may be taken.
        const lng = xs.length;
        let i = 0;

        while (true) {
            yield xs[i];
            i = (1 + i) % lng;
        }
    };


    // length :: [a] -> Int
    const length = xs =>
        // Returns Infinity over objects without finite
        // length. This enables zip and zipWith to choose
        // the shorter argument when one is non-finite,
        // like cycle, repeat etc
        "GeneratorFunction" !== xs.constructor
        .constructor.name ? (
            xs.length
        ) : Infinity;


    // subtract :: Num -> Num -> Num
    const subtract = x =>
        y => y - x;


    // tail :: [a] -> [a]
    const tail = xs =>
        // A new list consisting of all
        // items of xs except the first.
        "GeneratorFunction" !== xs.constructor
        .constructor.name ? (
            Boolean(xs.length) ? (
                xs.slice(1)
            ) : undefined
        ) : (take(1)(xs), xs);


    // take :: Int -> [a] -> [a]
    // take :: Int -> String -> String
    const take = n =>
        // The first n elements of a list,
        // string of characters, or stream.
        xs => "GeneratorFunction" !== xs
        .constructor.constructor.name ? (
            xs.slice(0, n)
        ) : Array.from({
            length: n
        }, () => {
            const x = xs.next();

            return x.done ? [] : [x.value];
        }).flat();


    // uncurry :: (a -> b -> c) -> ((a, b) -> c)
    const uncurry = f =>
        // A function over a pair, derived
        // from a curried function.
        (...args) => {
            const [x, y] = Boolean(args.length % 2) ? (
                args[0]
            ) : args;

            return f(x)(y);
        };


    // zip :: [a] -> [b] -> [(a, b)]
    const zip = xs => ys => {
        const
            n = Math.min(length(xs), length(ys)),
            vs = take(n)(ys);

        return take(n)(xs)
            .map((x, i) => [x, vs[i]]);
    };


    // MAIN ---
    return main();
})();</syntaxhighlight>
{{Out}}
<pre>Polygonal area by shoelace formula:
[[3,4],[5,11],[12,8],[9,5],[5,6]] -> 30</pre>

=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''

===={{trans|Wren}}====
<syntaxhighlight lang="jq"># jq's length applied to a number is its absolute value.
def shoelace:
  . as $a
  | reduce range(0; length-1) as $i (0;
      . + $a[$i][0]*$a[$i+1][1] - $a[$i+1][0]*$a[$i][1] )
  | (. + $a[-1][0]*$a[0][1] - $a[0][0]*$a[-1][1])|length / 2;

[ [3, 4], [5, 11], [12, 8], [9, 5], [5, 6] ]
| "The polygon with vertices at \(.) has an area of \(shoelace)."</syntaxhighlight>
{{out}}
<pre>
The polygon with vertices at [[3,4],[5,11],[12,8],[9,5],[5,6]] has an area of 30.
</pre>
===={{trans|Julia}}====
<syntaxhighlight lang="jq">def zip_shoelace:
   def sumprod: reduce .[] as [$x,$y] (0; . + ($x * $y));
   . as {$x, $y}
   | [$x, ($y[1:] + [$y[0]])] | transpose | sumprod as $a
   | [($x[1:] + [$x[0]]), $y] | transpose | sumprod as $b
   | ($a - $b) | length / 2;

{x: [3, 5, 12, 9, 5], y: [4, 11, 8, 5, 6] }
| zip_shoelace</syntaxhighlight>
{{out}}
As above.

=={{header|Julia}}==
{{works with|Julia|0.6}}
{{trans|Python}}

<syntaxhighlight lang="julia">"""
Assumes x,y points go around the polygon in one direction.
"""
shoelacearea(x, y) =
    abs(sum(i * j for (i, j) in zip(x, append!(y[2:end], y[1]))) -
        sum(i * j for (i, j) in zip(append!(x[2:end], x[1]), y))) / 2

x, y = [3, 5, 12, 9, 5], [4, 11, 8, 5, 6]
@show x y shoelacearea(x, y)</syntaxhighlight>

{{out}}
<pre>x = [3, 5, 12, 9, 5]
y = [4, 11, 8, 5, 6]
shoelacearea(x, y) = 30.0</pre>

=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// version 1.1.3

class Point(val x: Int, val y: Int) {
    override fun toString() = "($x, $y)"
}
 
fun shoelaceArea(v: List<Point>): Double {
    val n = v.size
    var a = 0.0
    for (i in 0 until n - 1) { 
        a += v[i].x * v[i + 1].y - v[i + 1].x * v[i].y
    }
    return Math.abs(a + v[n - 1].x * v[0].y - v[0].x * v[n -1].y) / 2.0  
}

fun main(args: Array<String>) {
    val v = listOf(
        Point(3, 4), Point(5, 11), Point(12, 8), Point(9, 5), Point(5, 6)
    )
    val area = shoelaceArea(v) 
    println("Given a polygon with vertices at $v,")
    println("its area is $area")
}</syntaxhighlight>

{{out}}
<pre>
Given a polygon with vertices at [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
its area is 30.0
</pre>

=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
{def shoelace
 {lambda {:pol}
  {abs
   {/ 
    {- 
     {+ {S.map {{lambda {:pol :i} {* {car {A.get :i :pol}}
                                     {cdr {A.get {+ :i 1} :pol}}}} :pol}
               {S.serie 0 {- {A.length :pol} 2}}}
                                  {* {car {A.get {- {A.length :pol} 1} :pol}}
                                     {cdr {A.get 0 :pol}}}}
     {+ {S.map {{lambda {:pol :i} {* {car {A.get {+ :i 1} :pol}}
                                     {cdr {A.get :i :pol}}}} :pol}
               {S.serie 0 {- {A.length :pol} 2}}} 
                                  {* {car {A.get 0 :pol}}
                                     {cdr {A.get {- {A.length :pol} 1} :pol}}}}} 2}}}}
-> shoelace

{def pol
  {A.new {cons 3 4}
         {cons 5 11}
         {cons 12 8}
         {cons 9 5}
         {cons 5 6}}}
-> pol = [(3 4),(5 11),(12 8),(9 5),(5 6)]

{shoelace {pol}}
-> 30
</syntaxhighlight>

=={{header|Lua}}==
<syntaxhighlight lang="lua">function shoeArea(ps)
  local function det2(i,j)
    return ps[i][1]*ps[j][2]-ps[j][1]*ps[i][2]
  end
  local sum = #ps>2 and det2(#ps,1) or 0
  for i=1,#ps-1 do sum = sum + det2(i,i+1)end
  return math.abs(0.5 * sum)
end</syntaxhighlight>
Using an accumulator helper inner function
<syntaxhighlight lang="lua">function shoeArea(ps)
  local function ssum(acc, p1, p2, ...)
    if not p2 or not p1 then
      return math.abs(0.5 * acc)
    else
      return ssum(acc + p1[1]*p2[2]-p1[2]*p2[1], p2, ...)
    end
  end
  return ssum(0, ps[#ps], table.unpack(ps))
end

local p = {{3,4}, {5,11}, {12,8}, {9,5}, {5,6}}
print(shoeArea(p))-- 30 </syntaxhighlight>
both version handle special cases of less than 3 point as 0 area result.

=={{header|Maple}}==

<syntaxhighlight lang="maple">
with(ArrayTools):

module Point()
 option object;
 local x := 0;
 local y := 0;

 export getX::static := proc(self::Point, $)
  return self:-x;
 end proc;

 export getY::static := proc(self::Point, $)
  return self:-y
 end proc;

 export ModuleApply::static := proc()
  Object(Point, _passed);
 end proc;

 export ModuleCopy::static := proc(new::Point, proto::Point, X, Y, $)
  new:-x := X;
  new:-y := Y;
 end proc;

 export ModulePrint::static := proc(self::Point)
  return cat("(", self:-x, ",", self:-y, ")");
 end proc;
end module:

module Polygon()
 option object;
 local vertices := Array([Point(0,0)]);

 export getVertices::static := proc(self::Polygon)
  return self:-vertices;
 end proc;

 export area::static := proc(self::Polygon)
  local i, N := ArrayNumElems(self:-vertices);
  local total := getX(self:-vertices[N]) * getY(self:-vertices[1]) - getX(self:-vertices[1]) * getY(self:-vertices[N]);
  total += map(`+`, seq(getX(self:-vertices[i]) * getY(self:-vertices[i+1]), i = 1..(N-1))) - map(`+`, seq(getX(self:-vertices[i+1]) * getY(self:-vertices[i]), i = 1..(N-1)));
  return abs(total / 2);
 end proc;

 export ModuleApply::static := proc()
  Object(Polygon, _passed);
 end proc;

 export ModuleCopy::Static := proc(new::Polygon, proto::Polygon, Ps, $)
  new:-vertices := Ps;
 end proc;

 export ModulePrint::static := proc(self::Polygon)
  return self:-vertices;
 end proc;
end module:

P1 := Polygon(Array([Point(3,4), Point(5,11), Point(12,8), Point(9,5), Point(5,6)])):
area(P1);                                                                                               
</syntaxhighlight>

{{out}}<pre>
                                      30
</pre>

=={{header|Mathematica}}/{{header|Wolfram Language}}==
Geometry objects built-in in the Wolfram Language
<syntaxhighlight lang="mathematica">Area[Polygon[{{3, 4}, {5, 11}, {12, 8}, {9, 5}, {5, 6}}]]</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|min}}==
{{works with|min|0.19.3}}
<syntaxhighlight lang="min">((((first) map) ((last) map)) cleave) :dezip
(((first) (rest)) cleave append) :rotate
((0 <) (-1 *) when) :abs

(
  =b =a a size :n 0 :i () =list
  (i n <) (
    a i get b i get ' prepend list append #list
    i succ @i
  ) while list
) :rezip

(rezip (-> *) map sum) :cross-sum

(
  ((dezip rotate) (dezip swap rotate)) cleave
  ((id) (cross-sum) (id) (cross-sum)) spread
  - abs 2 /
) :shoelace

((3 4) (5 11) (12 8) (9 5) (5 6)) shoelace print</syntaxhighlight>
{{out}}
<pre>
30.0
</pre>

=={{header|MiniScript}}==
<syntaxhighlight lang="miniscript">shoelace = function(vertices)
    sum = 0
    points = vertices.len
    
    for i in range(0,points-2)
        sum = sum + vertices[i][0]*vertices[i+1][1]
    end for
    sum = sum + vertices[points-1][0]*vertices[0][1]
    
    for i in range(points-1,1)
        sum = sum - vertices[i][0]*vertices[i-1][1]
    end for
    sum = sum - vertices[0][0]*vertices[points-1][1]
    
    return abs(sum)/2
end function

verts = [[3,4],[5,11],[12,8],[9,5],[5,6]]

print "The polygon area is "  + shoelace(verts)
</syntaxhighlight>
{{out}}
<pre>
The polygon area is 30
</pre>

=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">MODULE ShoelaceFormula;
FROM RealStr IMPORT RealToStr;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

TYPE
    Point = RECORD
        x,y : INTEGER;
    END;

PROCEDURE PointToString(self : Point; VAR buf : ARRAY OF CHAR);
BEGIN
    FormatString("(%i, %i)", buf, self.x, self.y);
END PointToString;

PROCEDURE ShoelaceArea(v : ARRAY OF Point) : REAL;
VAR
    a : REAL;
    i,n : INTEGER;
BEGIN
    n := HIGH(v);
    a := 0.0;
    FOR i:=0 TO n-1 DO
        a := a + FLOAT(v[i].x * v[i+1].y - v[i+1].x * v[i].y);
    END;
    RETURN ABS(a + FLOAT(v[n].x * v[0].y - v[0].x * v[n].y)) / 2.0;
END ShoelaceArea;

VAR
    v : ARRAY[0..4] OF Point;
    buf : ARRAY[0..63] OF CHAR;
    area : REAL;
    i : INTEGER;
BEGIN
    v[0] := Point{3,4};
    v[1] := Point{5,11};
    v[2] := Point{12,8};
    v[3] := Point{9,5};
    v[4] := Point{5,6};
    area := ShoelaceArea(v);

    WriteString("Given a polygon with verticies ");
    FOR i:=0 TO HIGH(v) DO
        PointToString(v[i], buf);
        WriteString(buf);
        WriteString(" ");
    END;
    WriteLn;

    RealToStr(area, buf);
    WriteString("its area is ");
    WriteString(buf);
    WriteLn;

    ReadChar;
END ShoelaceFormula.</syntaxhighlight>

=={{header|Nim}}==
<syntaxhighlight lang="nim">type
  Point = tuple
    x: float
    y: float

func shoelace(points: openArray[Point]): float =
  var leftSum, rightSum = 0.0
  for i in 0..<len(points):
    var j = (i + 1) mod len(points)
    leftSum  += points[i].x * points[j].y
    rightSum += points[j].x * points[i].y
  0.5 * abs(leftSum - rightSum)

var points = [(3.0, 4.0), (5.0, 11.0), (12.0, 8.0), (9.0, 5.0), (5.0, 6.0)]

echo shoelace(points)</syntaxhighlight>

{{out}}

<pre>30.0</pre>

=={{header|Perl}}==
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';

sub area_by_shoelace {
    my $area;
    our @p;
    $#_ > 0 ? @p = @_ : (local *p = shift);
    $area += $p[$_][0] * $p[($_+1)%@p][1] for 0 .. @p-1;
    $area -= $p[$_][1] * $p[($_+1)%@p][0] for 0 .. @p-1;
    return abs $area/2;
}

my @poly = ( [3,4], [5,11], [12,8], [9,5], [5,6] );

say area_by_shoelace(   [3,4], [5,11], [12,8], [9,5], [5,6]   );
say area_by_shoelace( [ [3,4], [5,11], [12,8], [9,5], [5,6] ] );
say area_by_shoelace(  @poly );
say area_by_shoelace( \@poly );</syntaxhighlight>
{{out}}
<pre>30
30
30
30</pre>

=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #008080;">enum</span> <span style="color: #000000;">X</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Y</span>
 <span style="color: #008080;">function</span> <span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
     <span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)></span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
         <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
             <span style="color: #000000;">t</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">constant</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}</span>
 <span style="color: #0000FF;">?</span><span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
30
</pre>
An alternative solution, which does not need the X,Y enum, and gives the same output:
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #008080;">function</span> <span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
         <span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">j</span> <span style="color: #008080;">do</span>
             <span style="color: #000000;">t</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
             <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #008080;">constant</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}</span>
 <span style="color: #0000FF;">?</span><span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->

=={{header|PowerBASIC}}==
{{Trans|Visual Basic}}
<syntaxhighlight lang="powerbasic">#COMPILE EXE
#DIM ALL
#COMPILER PBCC 6

FUNCTION ShoelaceArea(x() AS DOUBLE, y() AS DOUBLE) AS DOUBLE
LOCAL i, j AS LONG
LOCAL Area AS DOUBLE

  j = UBOUND(x())
  FOR i = LBOUND(x()) TO UBOUND(x())
    Area += (y(j) + y(i)) * (x(j) - x(i))
    j = i
  NEXT i
  FUNCTION = ABS(Area) / 2
END FUNCTION

FUNCTION PBMAIN () AS LONG
  REDIM x(0 TO 4) AS DOUBLE, y(0 TO 4) AS DOUBLE
  ARRAY ASSIGN x() = 3, 5, 12, 9, 5
  ARRAY ASSIGN y() = 4, 11, 8, 5, 6
  CON.PRINT STR$(ShoelaceArea(x(), y()))
  CON.WAITKEY$
END FUNCTION</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|Python}}==
===Python: Explicit===
<syntaxhighlight lang="python">>>> def area_by_shoelace(x, y):
    "Assumes x,y points go around the polygon in one direction"
    return abs( sum(i * j for i, j in zip(x,             y[1:] + y[:1]))
               -sum(i * j for i, j in zip(x[1:] + x[:1], y            ))) / 2

>>> points = [(3,4), (5,11), (12,8), (9,5), (5,6)]
>>> x, y = zip(*points)
>>> area_by_shoelace(x, y)
30.0
>>> 
</syntaxhighlight>

===Python: numpy===
<syntaxhighlight lang="python">
# Even simpler:
# In python we can take an advantage of that x[-1] refers to the last element in an array, same as x[N-1].
# Introducing the index i=[0,1,2,...,N-1]; i-1=[-1,0,...,N-2]; N is the number of vertices of a polygon.
# Thus x[i] is a sequence of the x-coordinate of the polygon vertices, x[i-1] is the sequence shifted by 1 index.
# Note that the shift must be negative. The positive shift x[i+1] results in an error: x[N] index out of bound.

import numpy as np
# x,y are arrays containing coordinates of the polygon vertices
x=np.array([3,5,12,9,5]) 
y=np.array([4,11,8,5,6]) 
i=np.arange(len(x))
#Area=np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5 # signed area, positive if the vertex sequence is counterclockwise
Area=np.abs(np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5) # one line of code for the shoelace formula

# Remember that applying the Shoelace formula
# will result in a loss of precision if x,y have big offsets.
# Remove the offsets first, e.g. 
# x=x-np.mean(x);y=y-np.mean(y)
# or
# x=x-x[0];y=y-y[0]
# before applying the Shoelace formula.   

</syntaxhighlight>

===Python: Defined in terms of reduce and cycle===
{{Trans|Haskell}}
{{Works with|Python|3.7}}
<syntaxhighlight lang="python">'''Polygonal area by shoelace formula'''

from itertools import cycle, islice
from functools import reduce
from operator import sub

# --------- SHOELACE FORMULA FOR POLYGONAL AREA ----------

# shoelaceArea :: [(Float, Float)] -> Float
def shoelaceArea(xys):
    '''Area of polygon with vertices
       at (x, y) points in xys.
    '''
    def go(a, tpl):
        l, r = a
        (x, y), (dx, dy) = tpl
        return l + x * dy, r + y * dx

    return abs(sub(*reduce(
        go,
        zip(
            xys,
            islice(cycle(xys), 1, None)
        ),
        (0, 0)
    ))) / 2


# ------------------------- TEST -------------------------
# main :: IO()
def main():
    '''Sample calculation'''

    ps = [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)]
    print(__doc__ + ':')
    print(repr(ps) + '  ->  ' + str(shoelaceArea(ps)))


if __name__ == '__main__':
    main()</syntaxhighlight>
{{Out}}
<pre>Polygonal area by shoelace formula:
[(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)]  ->  30.0</pre>

===Python: Alternate===
This adopts the ''indexing'' used in the numpy example above, but does not require the numpy library.
<syntaxhighlight lang="python">>>> def area_by_shoelace2(x, y):
	return abs(sum(x[i-1]*y[i]-x[i]*y[i-1] for i in range(len(x)))) / 2.

>>> points = [(3,4), (5,11), (12,8), (9,5), (5,6)]
>>> x, y = zip(*points)
>>> area_by_shoelace2(x, y)
30.0
>>> </syntaxhighlight>

=={{header|Racket}}==
<syntaxhighlight lang="racket">#lang racket/base

(struct P (x y))

(define (area . Ps)
  (define (A P-a P-b)
    (+ (for/sum ((p_i Ps)
                 (p_i+1 (in-sequences (cdr Ps)
                                      (in-value (car Ps)))))
         (* (P-a p_i) (P-b p_i+1)))))
  (/ (abs (- (A P-x P-y) (A P-y P-x))) 2))

(module+ main
  (area (P 3 4) (P 5 11) (P 12 8) (P 9 5) (P 5 6)))</syntaxhighlight>

{{out}}
<pre>30</pre>

=={{header|Raku}}==
(formerly Perl 6)
===Index and mod offset===
{{works with|Rakudo|2017.07}}

<syntaxhighlight lang="raku" line>sub area-by-shoelace(@p) {
    (^@p).map({@p[$_;0] * @p[($_+1)%@p;1] - @p[$_;1] * @p[($_+1)%@p;0]}).sum.abs / 2
}

say area-by-shoelace( [ (3,4), (5,11), (12,8), (9,5), (5,6) ] );</syntaxhighlight>
{{out}}
<pre>30</pre>

===Slice and rotation===
{{works with|Rakudo|2017.07}}
<syntaxhighlight lang="raku" line>sub area-by-shoelace ( @p ) {
    my @x := @p».[0];
    my @y := @p».[1];

    my $s := ( @x Z* @y.rotate( 1) ).sum
           - ( @x Z* @y.rotate(-1) ).sum;

    return $s.abs / 2;
}

say area-by-shoelace( [ (3,4), (5,11), (12,8), (9,5), (5,6) ] );
</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|REXX}}==
<!--
===endpoints as exceptions===
<syntaxhighlight lang="rexx">/*REXX program uses a  Shoelace  formula to calculate the area of an  N-sided  polygon. */
parse arg pts;           $polygon = 'polygon area of '  /*get optional args from the CL.*/
if pts=''  then pts= '(3,4),(5,11),(12,8),(9,5),(5,6)'  /*Not specified?   Use default. */
                         @= pts                         /*elide extra blanks;  save pts.*/
           do #=1  until @=''                           /*perform destructive parse on @*/
           parse var @  '('  x.#  ","  y.#  ')'  ","  @ /*obtain  X  and  Y  coördinates*/
           end   /*#*/
A= 0                                                    /*initialize the  area  to zero.*/
           do j=1  for #;  jp=j+1;  if jp>#   then jp=1 /*adjust for  J  for overflow.  */
                           jm=j-1;  if jm==0  then jm=# /*   "    "   "   "  underflow. */
           A=A + x.j * (y.jp - y.jm)                    /*compute a part of the area.   */
           end   /*j*/
say $polygon  #  " points: " pts '  is ───► '  abs(A/2) /*stick a fork in it, we're done*/</syntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
polygon area of  5  points:  (3,4),(5,11),(12,8),(9,5),(5,6)   is ───►  30
</pre>
!-->

=== wrap-around endpoints ===
<syntaxhighlight lang="rexx">/*REXX program uses  a  Shoelace  formula to calculate the area of an  N─sided  polygon.*/
parse arg $;  if $=''  then $= "(3,4),(5,11),(12,8),(9,5),(5,6)"      /*Use the default?*/
A= 0;                  @= space($, 0)                   /*init A; elide blanks from pts.*/
         do #=1  until @=='';      parse var  @    '('   x.#   ","   y.#   ')'   ","   @
         end   /*#*/                                    /* [↨]  get X and Y coördinates.*/
z= #+1;                 y.0= y.#;  y.z= y.1             /*define low & high Y end points*/
         do j=1  for #;  jm= j-1;  jp= j+1;   A= A + x.j*(y.jm - y.jp) /*portion of area*/
         end   /*j*/                                    /*stick a fork in it, we're done*/
say 'polygon area of '      #      " points: "       $       '  is ───► '        abs(A/2)</syntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
polygon area of  5  points:  (3,4),(5,11),(12,8),(9,5),(5,6)   is ───►  30
</pre>

===somewhat simplified===
reformatted and suitable for ooRexx. (x.0 etc. not needed)
<syntaxhighlight lang="text">/*REXX program uses a  Shoelace  formula to calculate the area of an  N-sided  polygon. */
parse arg pts                                    /*obtain optional arguments from the CL*/
if pts='' then pts= '(3,4),(5,11),(12,8),(9,5),(5,6)'   /*Not specified?   Use default. */
pts=space(pts,0); z=pts                                 /*elide extra blanks;  save pts.*/
do n=1 until z=''                                       /*perform destructive parse on z*/
  parse var z '(' x.n ',' y.n ')' ',' z                 /*obtain X and Y coördinates    */
  end
z=n+1; y.z=y.1                                          /* take care of end points      */
       y.0=y.n
A=0                                                     /*initialize the  area  to zero.*/
do j=1 for n;
  jp=j+1;
  jm=j-1;
  A=A+x.j*(y.jp-y.jm)                                   /*compute a part of the area.   */
  end
A=abs(A/2)                                              /*obtain half of the  ¦ A ¦  sum*/
say 'polygon area of' n 'points:' pts 'is --->' A</syntaxhighlight>
{{out}}
<pre>polygon area of 5 points: (3,4),(5,11),(12,8),(9,5),(5,6) is ---> 30</pre>

===even simpler===
Using the published algorithm
<syntaxhighlight lang="text">/*REXX program uses a  Shoelace  formula to calculate the area of an  N-sided  polygon. */
parse arg pts                                    /*obtain optional arguments from the CL*/
if pts='' then pts= '(3,4),(5,11),(12,8),(9,5),(5,6)'   /*Not specified?   Use default. */
pts=space(pts,0); z=pts                                 /*elide extra blanks;  save pts.*/
do n=1 until z=''                                       /*perform destructive parse on z*/
  parse var z '(' x.n ',' y.n ')' ',' z                 /*obtain X and Y coördinates    */
  end
a=0
Do i=1 To n-1
  j=i+1
  a=a+x.i*y.j-x.j*y.i
  End
a=a+x.n*y.1-x.1*y.n
a=abs(a)/2
say 'polygon area of' n 'points:' pts 'is --->' a</syntaxhighlight>
{{out}}
<pre>polygon area of 5 points: (3,4),(5,11),(12,8),(9,5),(5,6) is ---> 30</pre>

=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Shoelace formula for polygonal area

p = [[3,4], [5,11], [12,8], [9,5], [5,6]] 
see "The area of the polygon = " + shoelace(p)

func shoelace(p)
        sum = 0 
        for i = 1 to len(p) -1
             sum = sum + p[i][1] * p[i +1][2]
             sum = sum - p[i +1][1] * p[i][2]
        next
        sum = sum + p[i][1] * p[1][2]
        sum = sum - p[1][1] * p[i][2] 
        return fabs(sum) / 2
</syntaxhighlight>
Output:
<pre>
The area of the polygon = 30
</pre>

=={{header|RPL}}==
{| class="wikitable"
! RPL code
! Comment
|-
| 
 ≪ 
    DUP 1 GET +  
    0 2 3 PICK SIZE '''FOR''' j
       OVER j GET LAST 1 - GET
       OVER RE OVER IM * SWAP RE ROT IM * - +
    '''NEXT'''
    ABS 2 / SWAP DROP
 ≫ <span style="color:blue">''''SHOEL''''</span> STO
| 
 <span style="color:blue">'''SHOEL'''</span> ''( { (vertices) } → area ) ''
 append 1st vertice at the end
 sum = 0 ; loop 
   get 2 vertices
   sum += determinant 
   end loop
 finalize calculation, clean stack
 return area
|}
 {(3,4) (5,11) (12,8) (9,5) (5,6)} <span style="color:blue">'''SHOEL'''</span>
{{out}}
<pre>
1: 30
</pre>

=={{header|Ruby}}==
<syntaxhighlight lang="ruby">
Point = Struct.new(:x,:y) do

  def shoelace(other)
    x * other.y - y * other.x
  end

end

class Polygon

  def initialize(*coords)
    @points = coords.map{|c| Point.new(*c) } 
  end

  def area
    points = @points + [@points.first]
    points.each_cons(2).sum{|p1,p2| p1.shoelace(p2) }.abs.fdiv(2)
  end

end

puts Polygon.new([3,4], [5,11], [12,8], [9,5], [5,6]).area  # => 30.0
</syntaxhighlight>

=={{header|Scala}}==
<syntaxhighlight lang="scala">case class Point( x:Int,y:Int ) { override def toString = "(" + x + "," + y + ")" }

case class Polygon( pp:List[Point] ) {
  require( pp.size > 2, "A Polygon must consist of more than two points" )

  override def toString = "Polygon(" + pp.mkString(" ", ", ", " ") + ")"
  
  def area = {
  
    // Calculate using the Shoelace Formula
    val xx = pp.map( p => p.x )
    val yy = pp.map( p => p.y )
    val overlace = xx zip yy.drop(1)++yy.take(1)
    val underlace = yy zip xx.drop(1)++xx.take(1)
    
    (overlace.map( t => t._1 * t._2 ).sum - underlace.map( t => t._1 * t._2 ).sum).abs / 2.0
  }
}

// A little test...
{
val p = Polygon( List( Point(3,4), Point(5,11), Point(12,8), Point(9,5), Point(5,6) ) )

assert( p.area == 30.0 )

println( "Area of " + p + " = " + p.area )
}
</syntaxhighlight>
{{out}}
<pre>Area of Polygon( (3,4), (5,11), (12,8), (9,5), (5,6) ) = 30.0</pre>

=={{header|Sidef}}==
{{trans|Raku}}
<syntaxhighlight lang="ruby">func area_by_shoelace (*p) {
    var x = p.map{_[0]}
    var y = p.map{_[1]}

    var s = (
        (x ~Z* y.rotate(+1)).sum -
        (x ~Z* y.rotate(-1)).sum
    )

    s.abs / 2
}

say area_by_shoelace([3,4], [5,11], [12,8], [9,5], [5,6])</syntaxhighlight>
{{out}}
<pre>
30
</pre>

=={{header|Swift}}==

{{trans|Scala}}

<syntaxhighlight lang="swift">import Foundation

struct Point {
  var x: Double
  var y: Double
}

extension Point: CustomStringConvertible {
  var description: String {
    return "Point(x: \(x), y: \(y))"
  }
}

struct Polygon {
  var points: [Point]

  var area: Double {
    let xx = points.map({ $0.x })
    let yy = points.map({ $0.y })
    let overlace = zip(xx, yy.dropFirst() + yy.prefix(1)).map({ $0.0 * $0.1 }).reduce(0, +)
    let underlace = zip(yy, xx.dropFirst() + xx.prefix(1)).map({ $0.0 * $0.1 }).reduce(0, +)

    return abs(overlace - underlace) / 2
  }

  init(points: [Point]) {
    self.points = points
  }

  init(points: [(Double, Double)]) {
    self.init(points: points.map({ Point(x: $0.0, y: $0.1) }))
  }
}

let poly = Polygon(points: [
  (3,4),
  (5,11),
  (12,8),
  (9,5),
  (5,6)
])

print("\(poly) area = \(poly.area)")</syntaxhighlight>

{{out}}

<pre>Polygon(points: [Point(x: 3.0, y: 4.0), Point(x: 5.0, y: 11.0), Point(x: 12.0, y: 8.0), Point(x: 9.0, y: 5.0), Point(x: 5.0, y: 6.0)]) area = 30.0</pre>

=={{header|TI-83 BASIC}}==
{{works with|TI-83 BASIC|TI-84Plus 2.55MP}}
<syntaxhighlight lang="ti83b">[[3,4][5,11][12,8][9,5][5,6]]->[A]
Dim([A])->N:0->A
For(I,1,N)
    I+1->J:If J>N:Then:1->J:End
    A+[A](I,1)*[A](J,2)-[A](J,1)*[A](I,2)->A
End
Abs(A)/2->A</syntaxhighlight>
{{out}}
<pre>
          30
</pre>

=={{header|VBA}}==
{{trans|Phix}}<syntaxhighlight lang="vb">Option Base 1
Public Enum axes
    u = 1
    v
End Enum
Private Function shoelace(s As Collection) As Double
    Dim t As Double
    If s.Count > 2 Then
        s.Add s(1)
        For i = 1 To s.Count - 1
            t = t + s(i)(u) * s(i + 1)(v) - s(i + 1)(u) * s(i)(v)
        Next i
    End If
    shoelace = Abs(t) / 2
End Function
 
Public Sub polygonal_area()
    Dim task() As Variant
    task = [{3,4;5,11;12,8;9,5;5,6}]
    Dim tcol As New Collection
    For i = 1 To UBound(task)
        tcol.Add Array(task(i, u), task(i, v))
    Next i
    Debug.Print shoelace(tcol)
End Sub</syntaxhighlight>{{out}}
<pre>30</pre>

=={{header|VBScript}}==
<syntaxhighlight lang="vb">' Shoelace formula for polygonal area - VBScript
    Dim points, x(),y()
    points = Array(3,4, 5,11, 12,8, 9,5, 5,6)
    n=(UBound(points)+1)\2
    Redim x(n+1),y(n+1)
    j=0
    For i = 1 To n
        x(i)=points(j)
        y(i)=points(j+1)
        j=j+2
    Next 'i
    x(i)=points(0)
    y(i)=points(1)
    For i = 1 To n
        area = area + x(i)*y(i+1) - x(i+1)*y(i)
    Next 'i
    area = Abs(area)/2
    msgbox area,,"Shoelace formula" </syntaxhighlight>
{{out}}
<pre>
30
</pre>

=={{header|Visual Basic}}==
{{works with|Visual Basic|5}}
{{works with|Visual Basic|6}}
{{works with|VBA|Access 97}}
{{works with|VBA|6.5}}
{{works with|VBA|7.1}}
<syntaxhighlight lang="vb">Option Explicit

Public Function ShoelaceArea(x() As Double, y() As Double) As Double
Dim i As Long, j As Long
Dim Area As Double
 
  j = UBound(x())
  For i = LBound(x()) To UBound(x())
    Area = Area + (y(j) + y(i)) * (x(j) - x(i))
    j = i
  Next i
  ShoelaceArea = Abs(Area) / 2
End Function

Sub Main()
Dim v As Variant
Dim n As Long, i As Long, j As Long
  v = Array(3, 4, 5, 11, 12, 8, 9, 5, 5, 6)
  n = (UBound(v) - LBound(v) + 1) \ 2 - 1
  ReDim x(0 To n) As Double, y(0 To n) As Double
  j = 0
  For i = 0 To n
    x(i) = v(j)
    y(i) = v(j + 1)
    j = j + 2
  Next i
  Debug.Print ShoelaceArea(x(), y())
End Sub</syntaxhighlight>
{{out}}
<pre>30</pre>

=={{header|Visual Basic .NET}}==
{{trans|C#}}
<syntaxhighlight lang="vbnet">Option Strict On

Imports Point = System.Tuple(Of Double, Double)

Module Module1

    Function ShoelaceArea(v As List(Of Point)) As Double
        Dim n = v.Count
        Dim a = 0.0
        For i = 0 To n - 2
            a += v(i).Item1 * v(i + 1).Item2 - v(i + 1).Item1 * v(i).Item2
        Next
        Return Math.Abs(a + v(n - 1).Item1 * v(0).Item2 - v(0).Item1 * v(n - 1).Item2) / 2.0
    End Function

    Sub Main()
        Dim v As New List(Of Point) From {
            New Point(3, 4),
            New Point(5, 11),
            New Point(12, 8),
            New Point(9, 5),
            New Point(5, 6)
        }
        Dim area = ShoelaceArea(v)
        Console.WriteLine("Given a polygon with vertices [{0}],", String.Join(", ", v))
        Console.WriteLine("its area is {0}.", area)
    End Sub

End Module</syntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
its area is 30.</pre>

=={{header|Wren}}==
<syntaxhighlight lang="wren">var shoelace = Fn.new { |pts|
    var area = 0
    for (i in 0...pts.count-1) {
        area = area + pts[i][0]*pts[i+1][1] - pts[i+1][0]*pts[i][1]
    }
    return (area + pts[-1][0]*pts[0][1] - pts[0][0]*pts[-1][1]).abs / 2
}

var pts = [ [3, 4], [5, 11], [12, 8], [9, 5], [5, 6] ]
System.print("The polygon with vertices at %(pts) has an area of %(shoelace.call(pts)).")</syntaxhighlight>

{{out}}
<pre>
The polygon with vertices at [[3, 4], [5, 11], [12, 8], [9, 5], [5, 6]] has an area of 30.
</pre>

=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">proc real Shoelace(N, X, Y);
int     N, X, Y;
int     S, I;
[S:= 0;
for I:= 0 to N-2 do
        S:= S + X(I)*Y(I+1) - X(I+1)*Y(I);
S:= S + X(I)*Y(0) - X(0)*Y(I);
return float(abs(S)) / 2.0;
];

RlOut(0, Shoelace(5, [3, 5, 12, 9, 5], [4, 11, 8, 5, 6]))</syntaxhighlight>

{{out}}
<pre>
   30.00000
</pre>

=={{header|zkl}}==
By the "book":
<syntaxhighlight lang="zkl">fcn areaByShoelace(points){	// ( (x,y),(x,y)...)
   xs,ys:=Utils.Helpers.listUnzip(points); // (x,x,...), (y,y,,,)
   ( xs.zipWith('*,ys[1,*]).sum(0) + xs[-1]*ys[0] - 
     xs[1,*].zipWith('*,ys).sum(0) - xs[0]*ys[-1] )
   .abs().toFloat()/2;
}</syntaxhighlight>
or an iterative solution:
<syntaxhighlight lang="zkl">fcn areaByShoelace2(points){	// ( (x,y),(x,y)...)
   xs,ys:=Utils.Helpers.listUnzip(points); // (x,x,...), (y,y,,,)
   N:=points.len();
   N.reduce('wrap(s,n){ s + xs[n]*ys[(n+1)%N] - xs[(n+1)%N]*ys[n] },0)
   .abs().toFloat()/2;
}</syntaxhighlight>
<syntaxhighlight lang="zkl">points:=T(T(3,4), T(5,11), T(12,8), T(9,5), T(5,6));
areaByShoelace(points).println();
areaByShoelace2(points).println();</syntaxhighlight>
{{out}}
<pre>
30
30
</pre>