 Pick's theorem

For a simple polygon whose vertices are lattice points in ${\mathbb{Z}}^2$, its area is $A=I+B/2-1$, where $I$ counts interior lattice points and $B$ counts boundary lattice points.

Pick's Theorem provides a formula for determining the area of a simple lattice polygon (a polygon whose vertices are points with integer coordinates) based on the number of lattice points inside the polygon and on its boundary.