PK 2015 Q2
2. The diagram shows a square with sides of length \(a\). The shaded part of the square is bounded by a semicircle and two quarter-circle arcs.
What is the shaded area?
- A \(\dfrac{\pi a^2}{8}\)
- B \(\dfrac{a^2}{2}\)
- C \(\dfrac{\pi a^2}{2}\)
- D \(\dfrac{a^2}{4}\)
- E \(\dfrac{\pi a^2}{4}\)
Pink Kangaroo 2015, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B \(\dfrac{a^2}{2}\)
If the semicircle is cut into two quarter-circles, these can be placed next to the other shaded region to fill up half the square. Hence the shaded area is half of the area of the square, namely \(\tfrac{1}{2}a^2\).
Solution © UK Mathematics Trust, from the PK 2015 solutions.