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0580/12 Feb/Mar 2025, Question 14: Nets of 3D Shapes

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 7 marks

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The question, in short

For a triangular prism with isosceles triangle ABC (AC = BC, height 4 cm, AB = 6 cm) and BD = 6 cm, count faces and edges, show BC = 5 cm, and complete the net on a 1 cm² grid.

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

Part (a) · 2 marks

State how many faces and how many edges the triangular prism has.

  1. 1Faces: 2 triangles + 3 rectangles = 5
  2. 2Edges: 3 on each triangle + 3 joining them = 9

Answer5 faces and 9 edges

Part (b) · 2 marks

Use the isosceles triangle dimensions to show that BC equals 5 cm.

  1. 1The height bisects AB, so half of AB = 3 cm
  2. 2BC² = 3² + 4² = 9 + 16 = 25
  3. 3BC = √25 = 5 cm

Answer√(3² + 4²) [= 5]

Part (c) · 3 marks

Draw the remaining faces on the grid to complete the prism's net, given the 6 cm by 6 cm base.

  1. 1Draw a 6 cm by 5 cm rectangle on two opposite sides of the base (the sloping faces)
  2. 2On each of the other two sides draw a triangle with base 6 cm and apex 4 cm from the base, above its midpoint
  3. 3Check the triangle sides are 5 cm

AnswerCorrect net drawn: two 6 cm by 5 cm rectangles attached to opposite sides of the base, and two triangles (base 6 cm, height 4 cm, sloping sides 5 cm) on the other two sides

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Also searched as: 0580/12/F/M/25 · 0580_m25_qp_12 · 0580 m25 12 · question 14.
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