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0580/13 May/Jun 2022, Question 14: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 6 marks

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The question, in short

For an isosceles triangle with equal sides 5 cm and base 4 cm, find its height h, then use it to draw a net of a square-based pyramid on a 1 cm² grid.

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

Part (a) · 3 marks

Work out the vertical height h of the isosceles triangle from its side lengths.

  1. 1Half the base = 4 ÷ 2 = 2 cm
  2. 2h² = 5² − 2² = 25 − 4 = 21
  3. 3h = √21 = 4.582… ≈ 4.58 cm

Answer4.58 or 4.582 to 4.583

Part (b) · 3 marks

Using the triangle as one face, sketch a net of the square-based pyramid on the 1 cm² grid.

  1. 1Draw a 4 cm by 4 cm square
  2. 2On each side of the square draw an isosceles triangle with base 4 cm and sloping sides 5 cm (height about 4.6 cm)
  3. 3Use a ruler (compasses set to 5 cm help find each apex)

AnswerCorrect ruled net of the pyramid

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Also searched as: 0580/13/M/J/22 · 0580_s22_qp_13 · 0580 s22 13 · question 14.
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