I use this in measuring field areas. Like the text reads, this is Green's Theorem. The area of a triangle ABC can be determined by doing the cross product of a

I use this in measuring field areas. Like the text reads, this is Green's Theorem. The area of a triangle ABC can be determined by doing the cross product of any of the vectors that are the translation from a vertex to another (e.g. AB⨯AC = |AB|.|AC|.sin{^BAC}). More rigorously, this is the area of a lozenge, which then has to be divided by two. Imagining a point X inside a convex polygon, it is easy to see a set of triangles with vertex X in common. In fact, the polygon can not only be concave but point X can be outside the polygon, since the sine will compensate for negative and positive angles, subtracting any weird triangle out of the sum in the end. Computationally, the point X should be as close as possible to every vertex, so that rounding errors are minimized.