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0580/32 May/Jun 2026, Question 17: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Use the compound shape made from two rectangles with sides 12 cm, 6 cm, 9 cm and 7 cm to find its perimeter, the straight distance from X to Y, and the side of a square with equal area.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Work out the total perimeter of the compound shape.

  1. 1Missing sides: 9 − 6 = 3 cm and 12 − 7 = 5 cm
  2. 2Perimeter = 12 + 9 + 5 + 3 + 7 + 6
  3. 3= 42 cm

Answer42

Part (b) · 2 marks

Calculate the length of the straight line joining X to Y.

  1. 1Horizontal: 12 − 7 = 5 cm, vertical: 9 − 6 = 3 cm
  2. 2XY² = 5² + 3² = 34
  3. 3XY = √34 = 5.83 cm

Answer5.83 or 5.830 to 5.831

Part (c) · 3 marks

Find the side length of a square whose area equals the compound shape's area.

  1. 1Area = 12 × 9 − 7 × 3
  2. 2= 108 − 21 = 87 cm²
  3. 3Side = √87 = 9.33 cm

Answer9.33 or 9.327…

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Also searched as: 0580/32/M/J/26 · 0580_s26_qp_32 · 0580 s26 32 · question 17.
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