This activity shows how cutting geometric shapes and rearranging the pieces leads to some standard area formulas and to the Pythagorean Theorem. Complete proofs are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)