Lemmara logoLemmaraWorked solution

0580/43 Oct/Nov 2024, Question 7: Area of a Sector

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 15 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Calculate trapezium areas, form and solve a quadratic, find a sector perimeter, and find a composite shape area in the form a + kπ.

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

Part (ai) · 2 marks

Calculate area of trapezium with parallel sides 13 cm and 9 cm, height 8 cm.

  1. 1Area = 1/2 × (13 + 9) × 8
  2. 2= 88 cm²

Answer88

Part (aiia) · 3 marks

Use trapezium area formula with sides y + 4, y + 1, height y + 2, area 264 to derive 2y² + 9y − 518 = 0.

  1. 11/2 × (y + 4 + y + 1) × (y + 2) = 264
  2. 2(2y + 5)(y + 2) = 528
  3. 32y² + 4y + 5y + 10 = 528
  4. 42y² + 9y − 518 = 0

Answer1/2 (y + 4 + y + 1)(y + 2) = 264 leading to 2y² + 9y − 518 = 0

Part (aiib) · 3 marks

Factorise and solve 2y² + 9y − 518 = 0 to find y.

  1. 12y² + 9y − 518 = (2y + 37)(y − 14) = 0
  2. 2y = −37/2 or y = 14
  3. 3Length must be positive, so y = 14

Answer14

Part (b) · 3 marks

Find perimeter of sector with radius 8 cm and angle 75°.

  1. 1Arc = 75/360 × 2 × π × 8 = 10.47... cm
  2. 2Perimeter = 8 + 8 + 10.47... = 26.5 cm

Answer26.5 or 26.47...

Part (c) · 4 marks

Find area of shape ABQP, radius 5 cm, right angle at O, giving answer as a + kπ.

  1. 1OA² = 5² + 5² = 50
  2. 2Sector area = 90/360 × π × 50 = 25π/2
  3. 3Triangles APO and BQO = 2 × 1/2 × 5 × 5 = 25
  4. 4Area = 25 + 25π/2 cm²

Answer25 + 25π/2

Stuck on a step? Read the free lesson: Area of a Sector

Practise more area of a sector 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 area of a sector

Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.