UKMT Pink Kangaroo, 2022

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The bases of the two touching squares shown lie on the same straight line. The lengths of the diagonals of the larger square and the smaller square are $10$ cm and $8$ cm respectively. $P$ is the centre of the smaller square. What is the area, in cm $^2$ , of the shaded triangle $PQR$ ?

(A) $18$ (B) $20$ (C) $22$ (D) $24$ (E) $26$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.