Given a polygon with N vertices without any order, x0,y0 x1,y1 x2,y2 x3,y3 x4,y4 The area is given by A = 1 2 i = 0 N - 1 ( x i y i + 1 - x i + 1 y i ) , if the sign of the above expression is positive then the polygon vertices are ordered counter clockwise about the normal, otherwise clockwise.