I'd think the easiest way to do this would be to use a triangle fan, instead of a triangle strip. Then, you could just calculate the center of the polygon by "averaging" all of the vertices and create the fan starting at the center and going around through all of the corner vertices.

Of course, this relies on the polygon being convex; this won't always work with a concave polygon as the "center" may end up being outside of the polygon. If you need a more general solution, you should do some Google searches on triangulating polygons.

Here is the Wikipedia page on polygon triangulation if you need some general methods.