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What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Guillotine

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

$ABCD$ is a rectangle. $P$ is the midpoint of $AD$; the length of $BQ$ is one third the length of $BC$. What fraction of the area of the rectangle is the area of the shaded quadrilateral $ABQP$?
rectangle

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.


This problem is taken from the UKMT Mathematical Challenges.

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