Free polygon enumeration and the area of an integral polygon Original Research Article

We introduce the notion of free polygons as combinatorial building blocks for convex integral polygons; that is, polygons with vertices having integer coordinates. In this context, an Euler-type formula is derived for the number of integer points in the interior of an integral polygon. This leads in turn to a formula for the area of an integral polygon P via the enumeration of free integral triangles and parallelograms contained inside P.