The polygon below has vertices on an integer grid: it is a “lattice polygon”. What is its area? One approach is to add and subtract areas of rectangles and triangles surrounding the polygon. Pick’s theorem is another method, based on counting lattice points inside the polygon and on its boundary. The polygon has 5 lattice points inside it and 13 lattice points on its boundary. From these numbers alone, Pick’s theorem says that the area is 10 ½.

We will discuss Pick’s theorem and some applications. This is a good enrichment activity for future teachers.

NOTE: We are in a new room this semester!