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0606/22 Feb/Mar 2026, Question 5: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

For a badge made from three arcs centred on the vertices of an equilateral triangle of side x cm, find angle ABC in radians and then x given the badge area 2(π − √3) cm².

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

Part (a) · 1 mark

State the size of angle ABC of the equilateral triangle in radians, in terms of π.

  1. 1Each angle of an equilateral triangle is 60° = π/3 radians

Answerπ/3

Part (b) · 5 marks

Using the badge area 2(π − √3) cm², find the side length x.

  1. 1Area of triangle = (1/2)x² sin(π/3) = (√3/4)x²
  2. 2Area of each sector = (1/2)x²(π/3) = πx²/6
  3. 3Badge = 3 × sector − 2 × triangle
  4. 4= πx²/2 − (√3/2)x² = (x²/2)(π − √3)
  5. 5(x²/2)(π − √3) = 2(π − √3), so x² = 4, x = 2

Answerx = 2

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Also searched as: 0606/22/F/M/26 · 0606_m26_qp_22 · 0606 m26 22 · question 5.
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