You may also like

problem icon

Tri-split

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

problem icon

Areas and Ratios

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.

problem icon

Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Weekly Problem 9 - 2006

Stage: 4 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.

View the previous week's solution
View the current weekly problem