0606/22 Oct/Nov 2025, Question 2: The Cosine Rule
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
Shaded region ABCD has diagonals AC and BD of 12 cm bisecting at O, vertical parallel sides AD and BC of 4 cm, and arcs AB and DC centred at O. Find angle AOB in radians, then perimeter and area.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Find the obtuse angle AOB in radians, using the diagonals bisecting at O and the parallel sides of length 4 cm.
- 1OA = OB = OC = OD = 6 cm
- 2In triangle BOC: sin(½ angle BOC) = 2/6 = 1/3, so angle BOC = 2 sin⁻¹(1/3) = 0.6796…
- 3Angle AOB = π − angle BOC
- 4= π − 0.6796… = 2.46 radians
Answer2.46 radians
Part (bi) · 2 marks
Using the angle from part (a), find the perimeter of the shaded region ABCD, including arcs AB and DC.
- 1Arc AB = arc DC = 6 × 2.4619… = 14.77…
- 2Perimeter = 2 × 14.77… + 4 + 4
- 3= 37.5 cm
Answer37.5 cm
Part (bii) · 3 marks
Using the angle from part (a), find the area of the shaded region ABCD.
- 1Two sectors AOB and DOC: 2 × ½ × 6² × 2.4619… = 88.63…
- 2Two triangles AOD and BOC: 2 × ½ × 6² × sin 0.6796… = 22.63…
- 3Area = 88.63… + 22.63…
- 4= 111 cm²
Answer111 cm²
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Also searched as: 0606/22/O/N/25 · 0606_w25_qp_22 · 0606 w25 22 · question 2.
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