PK 2018 Q11
11. Eight congruent semicircles are drawn inside a square of side-length 4. Each semicircle begins at a vertex of the square and ends at a midpoint of an edge of the square. What is the area of the non-shaded part of the square?
- A \(2\pi\)
- B \(3\pi + 2\)
- C 8
- D \(6 + \pi\)
- E \(3\pi\)

Pink Kangaroo 2018, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 8
In the diagram the square of side-length 4 has been dissected into squares of side-length 1. The small curved pieces have then been moved as indicated by the arrows. The resulting shaded area consists of eight squares each with area 1, and the non-shaded area is the same.

Solution © UK Mathematics Trust, from the PK 2018 solutions.