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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) : Mathematics, 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.

### What is the Pick Theorem?

Pick's theorem simply 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 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. Thearea $$A$$ of the polygon is$$A = i + \ frac {b} {2} - 1$$

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