0580/42 Oct/Nov 2025, Question 7: Composite Perimeter, Area and Volume
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks
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The question, in short
Parallelogram with base 6.51 m and side x m has the same perimeter as a circle of radius 4 m; find x and the tiling cost at $18 per square metre.
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Part (a) · 4 marks
Use equal perimeters of the parallelogram and the circle with radius 4 m to show x = 6.06 m to 2 decimal places.
- 1Circumference = 2 × π × 4 = 8π = 25.132…
- 26.51 × 2 + 2x = 25.132…
- 32x = 25.132… − 13.02 = 12.112…
- 4x = 6.056… = 6.06 to 2 d.p.
Answer6.055 to 6.058
Part (b) · 4 marks
Using the 36° angle and side 6.06 m, find the parallelogram's area, then calculate the total tiling cost at $18 per square metre.
- 1Height = 6.06 × cos 36° = 4.9026…
- 2Area = 6.51 × 4.9026… = 31.916… m²
- 3Cost = 31.916… × 18 = 574.49… ≈ $574
Answer574 or 575 or 574.1 to 574.5…
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