GK 2015 Q13
13. One corner of a square is folded to its centre to form an irregular pentagon as shown in the diagram. The area of the square is 1 unit greater than the area of the pentagon. What is the area of the square?
- A 2
- B 4
- C 8
- D 16
- E 32
Grey Kangaroo 2015, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 8
The area of the darker triangle in the diagram is \(\tfrac{1}{8}\) of the area of the whole square and this also represents the difference between the area of the square and the area of the pentagon. Hence \(\tfrac{1}{8}\) of the area of the square is equal to 1 unit and so the area of the whole square is 8 units.
Solution © UK Mathematics Trust, from the GK 2015 solutions.