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polygon whose vertices have integer coordinates and whose area is 1/2

Source: Israel Grosman Memorial Mathematical Olympiad 1997 p2

February 15, 2020
geometrypolygonarealattice

Problem Statement

Is there a planar polygon whose vertices have integer coordinates and whose area is 1/21/2, such that this polygon is (a) a triangle with at least two sides longer than 10001000? (b) a triangle whose sides are all longer than 10001000? (c) a quadrangle?
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