Library / UKMT Intermediate Mathematical Challenge /194 of 267

UKMT Intermediate Mathematical Challenge, 2018

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a regular hexagon which has been divided into six regions by three of its diagonals. Two of these regions have been shaded. The total shaded area is $20\text{ cm}^2$ . What is the area of the hexagon?

(A) $40\text{ cm}^2$ (B) $48\text{ cm}^2$ (C) $52\text{ cm}^2$ (D) $54\text{ cm}^2$ (E) $60\text{ cm}^2$

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.