GK 2016 Q5
5. What is the total area in cm2 of the shaded region?
- A 50
- B 80
- C 100
- D 120
- E 150
Grey Kangaroo 2016, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 100
The area of the whole rectangle is 200 cm2. Suppose the rectangle is cut in two by a vertical cut joining the midpoints of its longer edges and the right-hand half is then given a quarter turn about its centre to produce the arrangement as shown. It can then be seen that every grey region has a corresponding white region of the same shape and size. Hence, the total area of the grey regions is half the area of the rectangle and so is 100 cm2.
Solution © UK Mathematics Trust, from the GK 2016 solutions.