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0580/12 May/Jun 2025, Question 13: Quadrilateral Properties

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 6 marks

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The question, in short

Identify a four-sided shape from its symmetry and equal sides, state rectangle properties, and draw a trapezium with parallel sides 6 cm and 4 cm and area 15 cm² on a 1 cm² grid.

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

Part (a) · 1 mark

Name the quadrilateral having four equal sides, two symmetry lines and rotational symmetry of order 2.

  1. 14 equal sides, 2 lines of symmetry, order 2: rhombus

Answerrhombus

Part (b) · 2 marks

Give two geometric features that every rectangle has.

  1. 1All four angles are 90°
  2. 2Opposite sides are equal and parallel

Answertwo properties stated that are better than any applying to all quadrilaterals.

Part (c) · 3 marks

On the 1 cm² grid, construct a trapezium whose parallel sides are 6 cm and 4 cm and whose area is 15 cm².

  1. 11/2 × (4 + 6) × h = 15
  2. 25h = 15, so h = 3 cm
  3. 3Draw parallel sides 6 cm and 4 cm, 3 cm apart, and join the ends

AnswerA correct drawing of a trapezium with perpendicular height 3cm and parallel sides 4cm and 6cm

Stuck on a step? Read the free lesson: Quadrilateral Properties

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Also searched as: 0580/12/M/J/25 · 0580_s25_qp_12 · 0580 s25 12 · question 13.
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