Pick’s theorem provides a formula for calculating the area of a polygon drawn on lattice points.
Formula
Pick’s formula for calculating the area A, is: A = \(\frac{P}{2}\) + Q – 1, where :
- P is the number of points on the polygonal chain;
- Q is the number of points located inside the polygon.
Example
A = \(\frac{P}{2}\) + Q – 1
A = \(\frac{9}{2}\) + 5 – 1
A = 4.5 + 5 – 1
A = 8.5