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0580/42 Oct/Nov 2025, Question 15: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Using a quadrilateral field diagram with diagonal BD and given side lengths and angle, find a side, an angle, and a perpendicular distance from D to AB given the total area.

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

Part (a) · 3 marks

Find the length of BC using triangle BDC with BD = 300 m, DC = 112 m and angle BDC = 140°.

  1. 1BC² = 300² + 112² − 2 × 300 × 112 × cos 140°
  2. 2BC² = 102 544 + 51 478.2… = 154 022.2…
  3. 3BC = √154 022.2… = 392.456… ≈ 392

Answer392 or 392.4 to 392.5

Part (b) · 3 marks

Find the size of angle DBC in triangle BDC.

  1. 1sin DBC / 112 = sin 140° / 392.456…
  2. 2sin DBC = 112 × sin 140° ÷ 392.456… = 0.18344…
  3. 3Angle DBC = 10.57…° ≈ 10.6°

Answer10.6 or 10.7 or 10.55 to 10.69

Part (c) · 4 marks

Given the field's total area is 35 900 m², work out the shortest distance from D to AB.

  1. 1Area BDC = 1/2 × 112 × 300 × sin 140° = 10 799.2… m²
  2. 2Area ABD = 35 900 − 10 799.2… = 25 100.7… m²
  3. 3Shortest distance from D to AB is the perpendicular height h of triangle ABD
  4. 41/2 × 180 × h = 25 100.7…
  5. 5h = 25 100.7… ÷ 90 = 278.89… ≈ 279 m

Answer279 or 278.9…

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