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0580/32 Oct/Nov 2022, Question 7: Area of a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Compare perimeters of rectangles A and B with equal areas, find a circle's radius from its area, and calculate an isosceles triangle's area from its sides.

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

Part (a) · 4 marks

Rectangle A is 2 cm by 12 cm; rectangle B has height 4 cm and the same area. Find which perimeter is greater and by how much.

  1. 1Area A = 2 × 12 = 24 cm², so length of B = 24 ÷ 4 = 6 cm
  2. 2Perimeter A = 2 × (2 + 12) = 28 cm
  3. 3Perimeter B = 2 × (4 + 6) = 20 cm
  4. 428 − 20 = 8: Rectangle A, by 8 cm

AnswerRectangle A, by 8 cm

Part (b) · 3 marks

A circle has area 150 cm². Calculate its radius.

  1. 1πr² = 150
  2. 2r² = 150 ÷ π = 47.74…
  3. 3r = √47.74… = 6.909… ≈ 6.91 cm

Answer6.91 or 6.909…

Part (c) · 5 marks

An isosceles triangle has base 12 cm and equal sides 16 cm. Find its area using the perpendicular height.

  1. 1The height bisects the base: half base = 6 cm
  2. 2h² = 16² − 6² = 220, h = 14.83… cm
  3. 3Area = 1/2 × 12 × 14.83… = 88.99… ≈ 89.0 cm²

Answer89.0 or 88.98 to 89

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Also searched as: 0580/32/O/N/22 · 0580_w22_qp_32 · 0580 w22 32 · question 7.
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