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area chasing in convex hexagon

Source: TOT 520 1996 Autumn S A3 Tournament Of Towns

August 16, 2024
geometryareashexagon

Problem Statement

Let A′,B′,C′,D′,E′A', B', C', D', E' and F′F' be the midpoints of the sides ABAB, BCBC, CDCD, DEDE, EFEF and FAFA of an arbitrary convex hexagon ABCDEFABCDEF respectively. Express the area of ABCDEFABCDEF in terms of the areas of the triangles ABCABC, BCD′BCD', CDS′CDS', DEF′DEF', EFA′EFA' and FAB′FAB'.
(A Lopshi tz, NB Vassiliev)
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