Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2021, Question 8: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use two right-angled triangle diagrams: in ABC find BC and angle BAC, then in a two-triangle shape with total area 246 cm² work out x.

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

Part (ai) · 2 marks

Right-angled triangle ABC has AB = 125 m and AC = 100 m; show that BC = 75 m.

  1. 1BC² + 100² = 125²
  2. 2BC² = 125² − 100² = 15625 − 10000 = 5625
  3. 3BC = √(125² − 100²) = √5625 = 75 m

Answer√(125² − 100²) = 75

Part (aii) · 2 marks

For the same triangle, calculate angle BAC.

  1. 1cos BAC = 100/125
  2. 2Angle BAC = 36.86… ≈ 36.9°

Answer36.9 or 36.86 to 36.87

Part (b) · 3 marks

Two right-angled triangles form a shape of total area 246 cm²; given sides 16 cm, 12 cm, 20 cm and x cm, find x.

  1. 1½ × 16 × 12 + ½ × 20 × x = 246
  2. 296 + 10x = 246
  3. 310x = 150, x = 15

Answer15

Stuck on a step? Read the free lesson: Composite Perimeter, Area and Volume

Practise more composite perimeter, area and volume questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on composite perimeter, area and volume

Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.