Radius of Gyration for Generic Polygons

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I need to calculate the radius of gyration for a generic, convex polygon, where the density is constant, the axis of rotation is the centroid (which is known), and the positions of the vertices are known. Does such an equation exist?

 

[A.T.]

http://en.wikipedia.org/wiki/Radius_of_gyration#Applications_in_mechanics
http://lab.polygonal.de/2006/08/17/calculating-the-moment-of-inertia-of-a-convex-polygon/

I would triangulate the two polygon parts separated by the axis individually. And then workout the inertial moment around that axis.