The properties of the cross section tell us a lot about how beams carry load, and they give us a way to think about how to design beams to do that task efficiently. In this chapter we delve into the computation of these geometric properties, first by setting up the relevant integrals and solving them directly, second by introducing a couple of integration tricks that can simplify the computation in certain cases, and finally by creating an algorithm and code that will compute the properties for any cross section with a polygonal shape (or a shape that can be approximated by a polygon).