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St Nicholas 2025 P6 Maths Prelim — Paper 2 Q17a Solution

Paper 2 · Q17a · 1 mark · Area and Perimeter

Question

A footpath of length 25.2 m is tiled using identical rectangular tiles and identical circular tiles, following the pattern shown. Each tile is in contact with those next to it. The width of the footpath is 84 cm. (Take $\pi = \frac{22}{7}$) (a) How many rectangular and circular tiles were used to tile the entire footpath altogether?
Answer: 280

Worked solution

  1. Footpath length $= 25.2\text{ m} = 2520\text{ cm}$. Each circular tile has diameter $84 \div 2 = 42\text{ cm}$, and one pattern block is $3 \times 42 = 126\text{ cm}$ long. Number of blocks $= 2520 \div 126 = 20$. Each block has $6 + 1 = 7$ tiles, so total $= 20 \times 7 = 140$ tiles per row, and with 2 rows, $140 \times 2 = 280$ tiles.

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