3D rectangle interaction with plane - Compute cut volume

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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!

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