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.




with javascript_semantics
enum X, Y
function shoelace(sequence s)
    atom t = 0
    if length(s)>2 then
        s = append(deep_copy(s),s[1])
        for i=1 to length(s)-1 do
            t += s[i][X]*s[i+1][Y] - s[i+1][X]*s[i][Y]
        end for
    end if
    return abs(t)/2
end function
 
constant test = {{3,4},{5,11},{12,8},{9,5},{5,6}}
?shoelace(test)
