3D rectangle interaction with plane - Compute cut volume

Hello,

Using Simmechanics, I have a 3D rectangle that I am intersecting with a plane at a known position. What I would like to know is the volume above and below that plane when my 3D rectangle is crossing the plane.

What would be the best approach to solve this problem?

I believe I could write equations of all cases depending on how the rectangle cuts the plane, but I hope there is a faster solution!

Thanks a lot!