Area in units of a GeneralPath

Is there a method to get the area (in units) of a closed GeneralPath or Area object?

For simple and convex shapes, work around the edge to create a large number of triangles (with one common point in the interior). Then add these up.
For simple, but nonconvex shapes ... there's always [Green's theorem|http://en.wikipedia.org/wiki/Planimeter]! Obtain a path iterator and integrate your way around the shape. Good luck with that.
In "Origin of Species" (written only a few years after the first working planimeter was constructed), Darwin estimates the forrested area of North America by cutting the map out of his atlas and weighing the bits.

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