The method is as follows:
- Begin by drawing a simple polygon on an equally spaced grid (i.e. graphing paper) so that all its vertices lie on grid points.
- Count the number of grid points, i, located in the interior of the polygon. Then, count the number of grid points, b, that fall on the boundary of the polygon.
A = i + b/2 - 1.
Note that this Theorem applies only to simple polygons, those with no holes and consisting only of one piece.
|i = 7, b = 8|
A = 7+8/2-1 = 10
A useful and handy application of this theorem is roughly estimating an area on a map (of say a region or country), by overlaying a grid and using a polygon to approximate the shape of the region you are interested in.