Surface Area of Solids · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Surface Area: Adding Up Every Face

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

  1. How many faces does a cuboid have?

    • 6
    • 4
    • 8
    • 5

  2. When you unfold a cuboid into a flat net, how many rectangular faces does it have?

    • 4
    • 6
    • 8

  3. Surface area only counts the faces you can see from the front, not the hidden ones.

    Circle one:   True   False

  4. A box face measures 3 cm by 4 cm. What is the area of that one face?

    • 7 cm2
    • 12 cm2
    • 24 cm2

  5. Which shapes make up the net of a square-based pyramid?

    • 1 square and 4 triangles
    • 4 squares and 1 triangle
    • 2 squares and 4 rectangles
    • 6 triangles

  6. A cuboid gift box is 20 cm long, 10 cm wide, and 15 cm tall. Which calculation finds the wrapping paper needed?

    • Add the six face areas: 2(20x10) + 2(20x15) + 2(10x15)
    • Multiply length x width x height
    • Add only the four side faces

  7. A cuboid measures 2 cm x 3 cm x 5 cm. What is its total surface area?

    • 31 cm2
    • 62 cm2
    • 56 cm2

  8. A cuboid measures 3 cm by 4 cm by 5 cm. What is its total surface area in square centimetres?

    Answer: ______________

  9. Priya finds the surface area of a square pyramid. She uses the square base (5 cm x 5 cm = 25 cm2) and adds one triangular face area three times, forgetting the pyramid has 4 triangular faces. What is wrong with her method?

    • She should not include the base at all
    • She used the wrong shape for the base
    • She left out one triangular face, so her total is too small

  10. A gift box measures 10 cm by 8 cm by 6 cm. What is its surface area in square centimetres?

    Answer: ______________

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Answer key

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

Surface Area: Adding Up Every Face W1-mt_hdhmurUndc-s1

  1. 6 · A cuboid has 6 rectangular faces: top and bottom, front and back, left and right.
  2. 6 · A cuboid has 6 rectangular faces: top, bottom, front, back, and two sides.
  3. False · Surface area covers every face of the solid, including the ones you cannot see, like the back and bottom.
  4. 12 cm2 · Multiply the two sides of the face: 3 x 4 = 12 cm2.
  5. 1 square and 4 triangles · A square base plus one triangle per side makes 1 square and 4 triangles.
  6. Add the six face areas: 2(20x10) + 2(20x15) + 2(10x15) · Wrapping paper covers every face, so you need the sum of all six face areas, not the volume or just some of the faces.
  7. 62 cm2 · The three different faces are 6, 10, and 15 cm2. Each appears twice, so 2 x (6+10+15) = 62 cm2.
  8. 94 · Faces pair up: 2 x (3x4 + 3x5 + 4x5) = 2 x 47 = 94 square centimetres.
  9. She left out one triangular face, so her total is too small · A square pyramid has 4 triangular faces, so leaving one out makes the surface area come out too small.
  10. 376 · Pairs give 2 x (10x8 + 10x6 + 8x6) = 2 x 188 = 376 square centimetres.
Worksheet · LightMySky