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0580/42 Oct/Nov 2021, Question 11: Area Factor of Similar Shapes

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Use similar triangles PQR and XYZ with given side lengths to find a missing side and an area, then use similar containers with given capacity and surface area to find a surface area.

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Part (ai) · 2 marks

Triangles PQR and XYZ are similar; PR = 20.4 cm, QR = 15.3 cm, XZ = 13.6 cm. Find YZ.

  1. 1YZ/15.3 = 13.6/20.4
  2. 2YZ = 15.3 × 13.6/20.4 = 10.2 cm

Answer10.2

Part (aii) · 3 marks

Area of triangle XYZ is 63.6 cm². Using the similarity, calculate the area of triangle PQR.

  1. 1Length scale factor XYZ → PQR = 20.4/13.6 = 1.5
  2. 2Area factor = 1.5² = 2.25
  3. 3Area PQR = 63.6 × 2.25 = 143.1 cm²

Answer143.1

Part (b) · 3 marks

Similar containers: larger capacity 64.8 litres, surface area 0.792 m²; smaller capacity 37.5 litres. Calculate the smaller surface area.

  1. 1Volume ratio small : large = 37.5/64.8 = 125/216
  2. 2Length ratio = ∛(125/216) = 5/6
  3. 3Area ratio = (5/6)² = 25/36
  4. 4Surface area = 0.792 × 25/36 = 0.55 m²

Answer0.55

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Also searched as: 0580/42/O/N/21 · 0580_w21_qp_42 · 0580 w21 42 · question 11.
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