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90 everywhere

Source: OMEC Ecuador National Olympiad Final Round 2022 N3 P3 day 1

November 2, 2024
geometryperimeternational olympiad

Problem Statement

A polygon is gridded if the internal angles of the polygon are either 9090 or 270270, it has integer side lengths and its sides don't intersect with each other. Prove that for all n≥8n \ge 8, it exist a gridded polygon with area 2n2n and perimeter 2n2n.
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