Edit:
Simple code I used to solve the problem in case anyone is interested (thanks to Fredrik):
int windowOverlap(Rectangle rect1, Rectangle rect
Maybe I misinterpret your question, but doesn't the Rectangle.Intersect method do the job? It returns the intersecting area, and then you can easily calculate the area of it.
Sounds like basic Collision Detection. Have you looked at this page on Wikipedia?
Mike
edit: Fredrik make his response at the same time I made this one, his answer got my upvote ( :