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16

Part of 2003 Romania Team Selection Test

Problems(1)

Given a convex hexagon and 6 triangle areas find its area

Source: Romanian IMO Team Selection Test TST 2004, problem 19

9/24/2005
Let ABCDEFABCDEF be a convex hexagon and denote by A′,B′,C′,D′,E′,F′A',B',C',D',E',F' the middle points of the sides ABAB, BCBC, CDCD, DEDE, EFEF and FAFA respectively. Given are the areas of the triangles ABC′ABC', BCD′BCD', CDE′CDE', DEF′DEF', EFA′EFA' and FAB′FAB'. Find the area of the hexagon. Kvant Magazine
geometry