St Nicholas 2025 P6 Maths Prelim — Paper 2 Q17b Solution

Paper 2 · Q17b · 3 marks · Area and Perimeter

Question

For the tiled footpath, (b) Find the area of the footpath not covered by tiles.

Answer: 15120 cm^2

There are $20 \times 2 = 40$ circular tiles. Each circular tile sits in a $42\text{ cm}$ square of area $42 \times 42 = 1764\text{ cm}^2$, while the circle has area $\frac{22}{7} \times 21 \times 21 = 1386\text{ cm}^2$. Uncovered area per circle $= 1764 - 1386 = 378\text{ cm}^2$. Total uncovered area $= 378 \times 40 = 15120\text{ cm}^2$.

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