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Surface Area

FoundationChallengeAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on surface area helps you revise calculating surface area. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Surface area is the total area of all the faces of a solid — start with cuboids.

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Topic overview

Surface area is the total area of all the faces of a three-dimensional shape. You find it by working out each face's area and adding them together.

For a cuboid there are three pairs of identical faces, so the surface area is \(2(lw + lh + wh)\). Finding one of each pair and doubling is quicker and less error-prone than calculating all six.

Because surface area is an area, the units are squared. This is the clearest way to distinguish it from volume, which uses cubed units, and confusing the two is the most common error in the topic.

Revision notes

Cuboids

A cuboid has three pairs of identical rectangular faces.

For a cuboid \(5 \times 3 \times 2\)cm: the pairs have areas \(15\), \(10\) and \(6\)cm², so the surface area is \(2(15 + 10 + 6) = 62\)cm².

Prisms

Work out the area of the two identical ends, then add the rectangles making up the sides.

Alternatively, the side area equals the perimeter of the end multiplied by the length of the prism, which is often quicker.

Working systematically

List each face, calculate its area, then add. Ticking them off ensures none is missed.

Sketching the net first makes the process visual and much harder to get wrong.

Key points

  • Surface area is the total area of all faces.
  • It is measured in squared units.
  • A cuboid has three pairs of identical faces.
  • Cuboid surface area is \(2(lw + lh + wh)\).
  • For a prism, use the perimeter times the length for the sides.
  • Sketch the net to avoid missing a face.

Worked examples

Example 1

Find the surface area of a cuboid \(6 \times 4 \times 3\)cm.

Working

\[6\times4=24 \text{, } 6\times3=18 \text{, } 4\times3=12\]find one face from each pair
\[24 + 18 + 12 = 54\]add the three areas
\[2 \times 54 = 108\text{cm}^2\]double for the matching pairs

Example 2

Find the surface area of a cube of side \(7\)cm.

Working

\[7 \times 7 = 49\text{cm}^2\]find the area of one face
\[49 \times 6\]a cube has six identical faces
\[= 294\text{cm}^2\]state the surface area

Example 3

A triangular prism has ends of area \(12\)cm² and side faces totalling \(90\)cm². Find the surface area.

Working

\[2 \times 12 = 24\]there are two identical ends
\[24 + 90\]add the side faces
\[= 114\text{cm}^2\]state the surface area

Common mistakes

  • Using cubed units.

    Surface area is an area, so cm² not cm³. Cubed units belong to volume.

  • Missing a face.

    Sketch the net or list the faces and tick them off as you calculate.

  • Forgetting to double the pairs on a cuboid.

    Each of the three face areas appears twice.

  • Confusing surface area with volume.

    Surface area adds face areas; volume multiplies three dimensions.

Exam tips

  • Sketch the net so every face is visible.
  • Find one of each pair and double for a cuboid.
  • Always use squared units.
  • Tick off each face as you calculate it.

Key terms

Surface area
The total area of all the faces.
Cuboid
A box shape with six rectangular faces.
Net
A flat layout of all the faces.
Squared units
Units such as cm² used for area.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.