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every convex n-gon of area 1 contains a quadrilateral of area at least 1/2

Source: Swedish Mathematical Competition 2004 p6

March 21, 2021
geometryGeometric Inequalitiesconvexareas

Problem Statement

Prove that every convex nn-gon of area 11 contains a quadrilateral of area at least 12\frac12 . .
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