Library / UKMT Intermediate Mathematical Challenge /255 of 267

UKMT Intermediate Mathematical Challenge, 2025

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

The diagram shows a rectangle which has been divided into four triangles. The areas, in cm $^2$ , of three of the triangles are as shown. What is the area of the shaded triangle?

(A) $11\text{ cm}^2$ (B) $13\text{ cm}^2$ (C) $14\text{ cm}^2$ (D) $15\text{ cm}^2$ (E) $16\text{ cm}^2$

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.