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St Nicholas 2025 P6 Maths Prelim — Paper 1 Booklet B Q29 Solution

Paper 1 Booklet B · Q29 · 2 marks · Area and Perimeter

Question

This figure is made up of 6 identical squares, a semicircle and an equilateral triangle. The width across the bottom of 4 squares is 24 cm. Find the perimeter of the figure. Leave your answer in terms of $\pi$.
Answer: $(6\pi + 72)$ cm

Worked solution

  1. Side of each square $= 24 \div 4 = 6\text{ cm}$. The semicircle has diameter $= 2 \times 6 = 12\text{ cm}$, so its arc $= \frac{1}{2} \times \pi \times 12 = 6\pi\text{ cm}$. The remaining straight edges total $6 \times 12 = 72\text{ cm}$. Perimeter $= (6\pi + 72)\text{ cm}$.

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