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Actually my solution is a formula already, which I came cross on some site. Using determinants to get the area of a polygon.
I think that is right, George.
Quickest and Absolute Accurate
Suppose you have n points on your polygon. And they are A1,A2,...An counterclockwise sequenced, also you know their positions in Cartesian co-ords.
I have written this up here: Area of Irregular Polygons
I did this once.
You have to decompose the figure. For example, if it's a triangle on top of a square, first find the area of the square, then the area of the triangle, and add them together.
I would divide your irregular shape into basic shapes, such as rectangles, trapazium, triangles, semicircles etc.