GK 2017 Q5
5. The diagram shows four overlapping hearts. The areas of the hearts are 1 cm2, 4 cm2, 9 cm2 and 16 cm2. What is the total shaded area?
- A 9 cm2
- B 10 cm2
- C 11 cm2
- D 12 cm2
- E 13 cm2
Grey Kangaroo 2017, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 10 cm2
Since the areas of the four hearts are 1 cm2, 4 cm2, 9 cm2 and 16 cm2, the outer and inner shaded regions have areas 16 cm2 − 9 cm2 = 7 cm2 and 4 cm2 − 1 cm2 = 3 cm2 respectively. Therefore the total shaded area is 7 cm2 + 3 cm2 = 10 cm2.
Solution © UK Mathematics Trust, from the GK 2017 solutions.