Given the n + 1 vertices x[0], y[0] .. x[N], y[N] of a simple polygon described in a clockwise direction, then the polygon's area can be calculated by:

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
(Where abs returns the absolute value)

Task

Write a function/method/routine to use the the Shoelace formula to calculate the area of the polygon described by the ordered points:

     (3,4), (5,11), (12,8), (9,5), and (5,6) 



Show the answer here, on this page.




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]))