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0580/31 May/Jun 2023, Question 4: Area of a Parallelogram and Trapezium

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

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The question, in short

Use a net drawn on a 1 cm² grid to identify matching vertices, work out surface area, name the solid and its cross-section, sketch it, then find x for a cuboid of volume 540 cm³ with edges 6 cm, 6 cm and x cm.

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

Part (ai) · 1 mark

Given that folding brings C onto A, state the remaining vertex that meets A.

  1. 1Edge AB folds onto edge BC, so C meets A
  2. 2Rectangle strip A−B−E−F−G wraps round, so edge GH meets edge AN
  3. 3G joins with A

AnswerG

Part (aii) · 3 marks

Work out the total area of all faces of the folded solid.

  1. 1Rectangles: 6 × 5 + 6 × 9 + 6 × 5 + 6 × 3 = 6 × 22 = 132
  2. 2Each trapezium: 1/2 × (9 + 3) × 4 = 24
  3. 3Two trapezia: 48
  4. 4Total = 132 + 48 = 180 cm²

Answer180

Part (aiii) · 2 marks

Fill the gaps naming the type of solid and the shape of its cross-section.

  1. 1The two end faces are congruent trapezia joined by rectangles
  2. 2So the solid is a prism with a trapezium cross-section

Answerprism, trapezium

Part (aiv) · 1 mark

Produce a rough drawing of the 3D solid formed from the net.

  1. 1Draw a trapezium for the front face
  2. 2Draw parallel edges going back from each vertex
  3. 3Join them to a second identical trapezium

AnswerA recognisable attempt at a prism with trapezium cross-section

Part (b) · 2 marks

Given a cuboid measuring 6 cm by 6 cm by x cm with volume 540 cm³, determine x.

  1. 16 × 6 × x = 540
  2. 236x = 540
  3. 3x = 15

Answer15

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Also searched as: 0580/31/M/J/23 · 0580_s23_qp_31 · 0580 s23 31 · question 4.
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