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.




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)).")