The area of a polygon with vertices on a planar integer lattice, as drawn below

2 interior and 7 boundary points

, equals $i+\frac{b}{2}-1$, where i denotes the number of lattice points interior to the polygon and b denotes the number of lattice points on the polygon’s boundary. In the diagram, i =  2 and b =  7, so that the area is 4½.