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Australian AMC 2016 - Senior Question 16

AMC AUSTRALIA · Australian AMC 2016 - Senior

Question 16

In the diagram, $QR=QT=4$ cm and $PQR$ and $QST$ are both isosceles right-angled triangles. In square centimetres, what is the area of the quadrilateral $QRXT$?

Question illustration
  1. $16(\sqrt2-1)$
  2. $4\sqrt2$
  3. $16\sqrt2-10$
  4. $8(\sqrt2-1)$
  5. $8-\sqrt2$