Although this has nothing to do with cross sections, it fits the physical materials:
You could have the students cut out shapes to illustrate constructive proofs of the Pythagorean theorem:
![enter image description here][1]
![enter image description here][2]
(Images from a [Steven Strogatz NYTimes article](http://opinionator.blogs.nytimes.com/2010/03/14/square-dancing/).)
Another constructive proof is described in [this MESE answer](http://matheducators.stackexchange.com/a/7203/511).