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Pick's Theorem

Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

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Pick's Theorem -

Tag(s) : Geometry

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Pick's Theorem

Pick Polygon Area Calculator



Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

Answers to Questions

What is the Pick Theorem?

Pick's theorem easily calculates the area of a polygon with $ b $ vertices built on a 2D grid of points with integer coordinates (points with equal distances). If all $ b $ vertices of the polygon (vertices can be flat) are grid points and the polygon has $ i $ points inside itself then Pick's formula indicates that the polygon area $ A $ is equal to $$ A = i + \frac{b}{2} - 1 $$

How to calculate an area with the Pick Theorem?

The Pick formula requires only two parameters: the number $ i $ of interior points of the polygon and the number $ b $ of vertices of the polygon (which is in the number of grid points on the perimeter of the polygon). Thearea $ A $ of the polygon is$ A = i + \ frac {b} {2} - 1 $

Example: The polygon drawn below example.png has 15 points inside the polygon (light gray), and 10 vertices (dark gray). Its area is therefore $ A = 15 + 10/2 - 1 = 19 $.

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