IMC 2018 Q11
11. 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 cm2.
What is the area of the hexagon?
- A 40 cm2
- B 48 cm2
- C 52 cm2
- D 54 cm2
- E 60 cm2
Intermediate Mathematical Challenge 2018, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 48 cm2
The diagram shows that the hexagon may be divided into twelve congruent triangles, of which five are shaded. Let the area of each of these triangles be \(a\) cm2. Then \(5a = 20\), so \(a = 4\). Hence the area of the hexagon, in cm2, is \(12a = 12 \times 4 = 48\).
Solution © UK Mathematics Trust, from the IMC 2018 solutions. Longer versions with investigations: Solutions and investigations (PDF).