RO-TST 2003 Problem 16

Let $ABCDEF$ be a convex hexagon and denote by $A',B',C',D',E',F'$ the middle points of the sides $AB$ , $BC$ , $CD$ , $DE$ , $EF$ and $FA$ respectively. Given are the areas of the triangles $ABC'$ , $BCD'$ , $CDE'$ , $DEF'$ , $EFA'$ and $FAB'$ . Find the area of the hexagon.

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