Pick's Theorem
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 = [latex]\frac{P}{2}[/latex] + 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 = [latex]\frac{P}{2}[/latex] + Q – 1
A = [latex]\frac{9}{2}[/latex] + 5 – 1
A = 4.5 + 5 – 1
A = 8.5