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## Pick's theorem

Let $P$ be a polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points. Let $I$ be the number of lattice points in the interior of $P$. Let $B$ be the number of lattice points on the boundary of $P$. Prove that the area $A$ of the polygon $P$ is given by

$A = I + B/2 - 1$

Source: folklore

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