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.




Option Base 1
Public Enum axes
    u = 1
    v
End Enum
Private Function shoelace(s As Collection) As Double
    Dim t As Double
    If s.Count > 2 Then
        s.Add s(1)
        For i = 1 To s.Count - 1
            t = t + s(i)(u) * s(i + 1)(v) - s(i + 1)(u) * s(i)(v)
        Next i
    End If
    shoelace = Abs(t) / 2
End Function
 
Public Sub polygonal_area()
    Dim task() As Variant
    task = [{3,4;5,11;12,8;9,5;5,6}]
    Dim tcol As New Collection
    For i = 1 To UBound(task)
        tcol.Add Array(task(i, u), task(i, v))
    Next i
    Debug.Print shoelace(tcol)
End Sub