Surface area

Objective. Calculate surface area from nets and dimensions.

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2. Worked example
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Learn: the key idea

Surface area is the total area of all the faces of a 3D shape, found by unfolding the solid into its net and adding together the area of each flat face. Identify each face's shape, calculate its area separately, then sum all the faces, remembering to count repeated identical faces such as two matching ends. For a cuboid measuring 4 cm × 3 cm × 2 cm, the six faces give a surface area of 2(4×3) + 2(4×2) + 2(3×2) = 24 + 16 + 12 = 52 cm². Always check no face is missed or double counted by picturing the net.

Worked example

Find the surface area of a cube with edge length 6 cm.

1 $Find the area of one face: 6 \times 6 = 36 cm²$
2 $Recall a cube has 6 identical faces$
3 $Multiply the face area by 6: 36 \times 6$
4 $The surface area is 216 cm²$

Answer: 216 cm²

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Common mistake. Pupils often forget that a cuboid has three pairs of matching faces, calculating only three faces instead of doubling each pair. Always multiply each unique face's area by 2 for the matching opposite face.

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