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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

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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

How to calculate an area with the Pick Theorem?

The Pick theorem applies only to a polygon constructed on a grid of points with integers coordinates (equal-distanced points). All vertices of the polygon are points of the grid and have integer coordinates.

The Pick formula gives the area with a simple calculation and requires only two parameters: the number \( i \) of interior points of the polygon and the number \( b \) of vertices of the polygon.

$$ A = i + \ frac {b} {2} - 1 $$

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

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