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.




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;
}