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.




 
# 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
 