Is there a way to get the area of two overlapping objects?

Essentially what I am trying to do is have an object that I can move and change the color of another object based on where those two objects are overlapping at runtime. I know you can dynamically change a texture at runtime so if I could find the area the two objects overlap, I would basically be set.

you can have a bounding box or sphere, and calculate the area yourself.
it does not have to be a real bounding box, it could be a conceptual one.