The study of plane geometry, in particular the computation of areas of simple polygons, is little explored in the classroom. Our aim here is to state and prove Pick s Theorem. We also present sever al examples and more than one proof. Simple polygons (which are not necessarily convex) receive special attention. We also consider some related results, such as the theorems of Jordan and Euler. It is hoped that this re e arch will contribute to the teaching of mathematics in a qualitative way.