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.

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