Picks theorem

Pick's theorem was first illustrated by Georg Alexander Pick in 1899. This theorem is used to find the area of the polygon in terms of square units. Area can be found by counting the lattice points in the inner and boundary of the polygon.

Area of the polygon can be written as

'i'represents the interior lattice points and 'b' represents the boundary lattice points.

This theorem demonstrated well for the simple polygons, means the polygons that doesn't have holes. Polygon with the holes in the boundary can be derived with the formula

Reeve tetrahedron (Polyhedron named after John reeve) proved that pick's theorem is not applicable to find the volume of polytope in three dimensions by counting its inner and outer boundary. But this theorem is widely applicable for finding the surface of the polyhedron.