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Geometry & Measures · Foundation & Higher

3D shapes & nets

You need to recognise and name 3D shapes, identify their faces, edges and vertices, and draw and interpret their nets. Euler's formula connects these properties.

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Key facts to remember

  • 1A net is a 2D shape that folds to make a 3D solid.
  • 2Cuboid: 6 faces, 12 edges, 8 vertices.
  • 3Triangular prism: 5 faces (2 triangles, 3 rectangles), 9 edges, 6 vertices.
  • 4Square-based pyramid: 5 faces, 8 edges, 5 vertices.
  • 5Euler's formula: Faces + Vertices − Edges = 2.
  • 6A cylinder has 2 circular faces, 1 curved surface, and no vertices.
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Worked examples

Example 1

A solid has 6 faces and 8 vertices. How many edges does it have? Use Euler's formula.

Working

  1. F + V − E = 2
  2. 6 + 8 − E = 2
  3. 14 − E = 2
  4. E = 12
Answer12 edges
Example 2

Draw a net for a triangular prism with an equilateral triangle of side 4 cm and length 6 cm.

Working

  1. The net consists of 2 equilateral triangles and 3 rectangles (each 4 × 6 cm)
  2. Draw a row of 3 rectangles side by side, then attach the two triangles to the top and bottom of the middle rectangle
Answer2 equilateral triangles + 3 rectangles (4 cm × 6 cm)
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Common mistakes

✗Drawing an invalid net — one that doesn't fold into the correct solid.
✗Miscounting faces by including curved surfaces as faces.
✗Misapplying Euler's formula by using the wrong values.
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Exam tips

✓To check a net, mentally fold it — all faces must join without overlap or gaps.
✓Learn faces, edges and vertices for common shapes: cube, cuboid, prism, pyramid.

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