Library / UKMT Junior Kangaroo /196 of 243

UKMT Junior Kangaroo, 2019

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the quadrilateral $PQRS$ , the length of $PQ$ is 11 cm, the length of $QR$ is 7 cm, the length of $RS$ is 9 cm and the length of $SP$ is 3 cm. Both $\angle QRS$ and $\angle SPQ$ are $90°$ . What is the area of the quadrilateral $PQRS$ ?

(A) $30$ cm $^2$ (B) $48$ cm $^2$ (C) $50$ cm $^2$ (D) $52$ cm $^2$ (E) $60$ cm $^2$

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.