to verify polygons theorem
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Theorem: If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
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Pick's Theorem states that if a polygon has vertices with integer coordinates (lattice points) then the area of the polygon is i + {1\over 2}p - 1 where i is the number of lattice points inside the polygon and p is the number of lattice points on the perimeter of the polygon.
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