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IMSO 2014 — Math Division — Essay Question 7

IMSO Maths · IMSO 2014 — Math Division — Essay

Question 7

Let $ABCD$ be a square with side length $10$ cm. Points $E,F,G,H$ are on sides $AB,BC,CD,DA$, respectively, such that $EG$ is parallel to $AD$ and $FH$ is parallel to $AB$. If $P$ is a point on $AE$ such that $PE=2$ cm and $Q$ is a point on $DH$ such that $HQ=3$ cm, what is the area, in cm², of quadrilateral $PFGQ$?