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Tao Nan 2025 P6 Maths Prelim — Paper 2 Q17b Solution

Paper 2 · Q17b · 3 marks · Area and Perimeter

Question

Figure 2 is formed by three similar-sized circles and three similar-sized squares. Line $AB$ passes through the centre of the three circles. The area of each square is 256 cm^2. Find the difference in area between the shaded and unshaded parts. (Take $\pi = 3.14$)
Answer: 748.8 $cm^2$

Worked solution

  1. $\sqrt{256} = 16$. Shaded = 7 quarters + 1 square
  2. Unshaded = 3 quarters + 1 square + 1 boomerang (1 square - 1 quarter). Difference = 4 quarters - 1 boomerang. 4 quarters = 1 circle = $3.14 \times 16 \times 16 = 803.84$. 1 boomerang = $256 - \frac{1}{4} \times 3.14 \times 16 \times 16 = 256 - 200.96 = 55.04$. Difference = $803.84 - 55.04 = 748.8$ cm^2.

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