3-D shapes (age 11+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Counting faces and picturing cross-sections

Mathematics · Geometry · ages 11-13
Name ______________________   Date ____________

  1. A square-based pyramid has five faces. How many vertices does it have?

    Answer: ______________

  2. How many faces, edges and vertices does a triangular prism have?

    • 5 faces, 9 edges, 6 vertices
    • 6 faces, 12 edges, 8 vertices
    • 5 faces, 8 edges, 5 vertices
    • 4 faces, 6 edges, 4 vertices

  3. How many vertices does a triangular prism have?

    • 5
    • 6
    • 9

  4. Slicing a cylinder straight across (horizontally) always produces a circle.

    Circle one:   True   False

  5. A triangular prism has 6 vertices. How many edges does it have?

    Answer: ______________

  6. A net has 6 identical squares joined together. Which solid will it fold into?

    • Cube
    • Square-based pyramid
    • Triangular prism

  7. How many edges does a square-based pyramid have?

    • 5
    • 8
    • 6
    • 12

  8. Tom says a net of 4 triangles folds into a square-based pyramid. Is Tom right?

    Circle one:   True   False

  9. A student says a net with 1 triangle and 3 rectangles will fold into a triangular prism. Is the net correct?

    • No, a triangular prism needs 2 triangles and 3 rectangles, not 1 triangle
    • Yes, that is exactly right
    • No, a triangular prism needs 3 triangles and 3 rectangles

  10. Which net folds into a triangular prism?

    • Six squares
    • One square and four triangles
    • Four triangles
    • Two triangles and three rectangles
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Counting faces and picturing cross-sections W1-mt_nRksLqt-iR-s1

  1. 5 · Four base corners plus one apex give 5 vertices.
  2. 5 faces, 9 edges, 6 vertices · Two triangle ends plus three rectangles give 5 faces, 9 edges and 6 vertices.
  3. 6 · A triangular prism has 6 vertices: 3 on each triangular end. 9 is the edge count, not the vertex count.
  4. True · A horizontal slice runs parallel to the circular base, so the cross-section matches the base: a circle.
  5. 9 · A triangular prism always has 9 edges.
  6. Cube · A cube has 6 square faces, so 6 squares is exactly the right number and shape to fold into one.
  7. 8 · Four base edges plus four sloping edges give 8.
  8. False · Tom is wrong: 4 triangles make a triangular pyramid; a square base needs a square.
  9. No, a triangular prism needs 2 triangles and 3 rectangles, not 1 triangle · A triangular prism has 2 triangular ends, not 1, so this net is missing a face.
  10. Two triangles and three rectangles · A triangular prism needs exactly two triangle ends and three rectangular sides.
Worksheet · LightMySky