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UKMT Senior Kangaroo, 2015

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a triangle $ABC$ with area $12$ cm $^2$ . The sides of the triangle are extended to points $P$ , $Q$ , $R$ , $S$ , $T$ and $U$ as shown so that $PA = AB = BS$ , $QA = AC = CT$ and $RB = BC = CU$ . What is the area (in cm $^2$ ) of hexagon $PQRSTU$ ?

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