ABSTRACT
Starting in elementary school, children learn about such important concepts in measurement as area and volume. These are measures that are used in our lives on a daily basis. Archimedes did some magnificent mathematics. His mind was always churning. This chapter shows how to find the area of polygonal figures. Pick's Theorem is concerned with finding the area of a polygon whose vertices are at lattice points. Around 1899 Georg Pick discovered a remarkable theorem showing how to do this that depends on nothing more than the number of lattice points on the boundary of the polygon and the number of interior lattice points of the polygon. The chapter discusses several methods for finding the area of figures. Although Pick's Theorem is an interesting and effective way of finding the area of polygons, it can only be used for very specialized figures whose vertices are at lattice points (or are at points in the plane whose coordinates are integers).
