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Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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Triangles' Triangle

Weekly Problem 27 - 2009
The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

Square in a Triangle

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

The diagram shows that triangle $XYZ$ may be divided into 9 congruent triangles. The square $PQRS$ is made up of 4 of these 9 triangles. Therefore, the ratio is $4:9$.

                                 Subdivided right-angled triangle circumscribing square

This problem is taken from the UKMT Mathematical Challenges.