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.




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])