The surface area of a prism is the sum of the area of all the faces.
The net of a prism can help find the surface area of a prism but can be time consuming.
Using known area facts the area of all the faces can be found and summed.
It is important to find the surface area systematically and efficiently.

Common misconception

Pupils can miss out some faces of the prism when calculating the surface area.

Encourage pupils to sketch out the net of the prism and label it clearly, to ensure that they include all faces in their calculation of the surface area. This will allow their answer to be checked more easily.

Keywords

Prism - A prism is a polyhedron with a base that is a polygon and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.
Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Net - The net of a 3D object is a 2D representation of its surfaces that can be folded up into the 3D object.

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Select the units that could be used for the surface area of a cuboid.

Correct answer: m²

mm³

km³

Correct answer: km²

Q2.

Here is a net of a cube. Which calculations correctly give the surface area of the cube?

Correct answer: 16 × 6

4 + 4 + 4 + 4 + 4 + 4

Correct answer: (4 × 4) × 6

4 × 6

Correct answer: (4 × 4) + (4 × 4) + (4 × 4) + (4 × 4) + (4 × 4) + (4 × 4)

Q3.

Here is a net of a cuboid. What is the surface area of the cuboid?

16 cm²

32 cm²

79 cm²

120 cm²

Correct answer: 158 cm²

Q4.

The diagram shows the plan view and front and side elevations of a cuboid. The surface area of the cuboid is m².

Correct Answer: 52

Q5.

The diagram shows an isometric drawing of a cuboid. The surface area of the cuboid is m².

Correct Answer: 448

Q6.

Starting with the cuboid with the smallest surface area, put these cuboids in order of surface area size.

1 - Blue cuboid: width 2 cm, height 8 cm and length 16 cm

2 - Red cuboid: width 4 cm, height 10 cm and length 10 cm

3 - Yellow cuboid: width 6 cm, height 8 cm and length 10 cm

4 - Purple cuboid: width 8 cm, height 8 cm and length 8 cm

Exit quiz

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6 Questions

Q1.

This prism has two congruent regular pentagonal faces and congruent rectangular faces.

Correct Answer: five, 5

Q2.

Jun takes some measurements from a cube. Match each measurement to its correct value.

Correct Answer:Volume,64 cm³

64 cm³

Correct Answer:Surface area,96 cm²

96 cm²

Correct Answer:Perimeter of cross-section,16 cm

16 cm

Correct Answer:Length of one side,4 cm

4 cm

Correct Answer:Area of cross-section,16 cm²

16 cm²

Q3.

The surface area of this octagonal prism is cm².

Correct Answer: 1214, 1,214, 1 214

Q4.

The diagram shows a prism unfolded into its net. The perimeter of the cross-sectional face is 80 cm. Which of these statements are correct?

Correct answer: Dimensions of rectangle in the net: 8 cm by 80 cm

Dimensions of rectangle in the net: 8 cm by 300 cm

Total surface area = (300 + 5 × 80) cm²

Total surface area = (2 × 300 + 5 × (80 × 8)) cm²

Correct answer: Total surface area = (2 × 300 + 80 × 8) cm²

Q5.

The diagram shows the net of a triangular prism. The depth of the prism is 2 cm. The surface area of the prism that can be formed from this net is cm².

Correct Answer: 36

Q6.

The cross-section of this prism is an equilateral triangle. The surface area of this triangular prism is cm². Give your answer correct to 3 significant figures.

Correct Answer: 269