Solid shapes · Usually met around P5
Surface area
Add the three different faces, then double.
How to do it
Method
Add the three different faces, then double
A 5 × 4 × 3 cuboid: (20 + 15 + 12) × 2 = 94
Another way
Add all 6 faces
20 + 20 + 15 + 15 + 12 + 12 = 94
In full
Surface area is the total area of all of a solid's faces: the area of its net once it is opened out flat. A cube has 6 equal squares: surface area = 6 × edge × edge. A cuboid's opposite faces match: work out the three different faces, length × width, length × height and width × height, add them and double: 5 × 4 = 20, 5 × 3 = 15, 4 × 3 = 12, (20 + 15 + 12) × 2 = 94 cm². Another way: add the 6 faces of the net one by one, 20 + 20 + 15 + 15 + 12 + 12 = 94, the same. A triangular prism = 2 triangles + 3 rectangles; a square pyramid = the square base + 4 triangles. Think first about which faces count: a box with no lid has one face fewer, and wallpaper covers only the four walls. Surface area is in square centimetres: don't mix it up with volume (cubic centimetres) or the total length of the edges (centimetres).
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A cuboid is 9 cm long, 11 cm wide and 13 cm high. What is its surface area, in cm²?
Show the answer and working
Answer: 718 cm²
The three different faces: 99, 117 and 143, adding to 359; there are 2 of each: 359 × 2 = 718.
Example 2
A cuboid is 16 cm long, 9 cm wide and 11 cm high. Which calculation gives its surface area?
- A. 4 × (16 + 9 + 11)
- B. 16 × 9 + 16 × 11 + 9 × 11
- C. 16 × 9 × 11
- D. 2 × (16 × 9 + 16 × 11 + 9 × 11)
Choose the right answer
Show the answer and working
Answer: D. 2 × (16 × 9 + 16 × 11 + 9 × 11)
A cuboid has 3 pairs of matching faces: 2 × (16 × 9 + 16 × 11 + 9 × 11) = 838.
Example 3
A triangular prism is 8 cm long. Its two ends are right-angled triangles with sides 3 cm, 4 cm and 5 cm (the 3 cm and 4 cm sides are at right angles). What is its surface area, in cm²?
Show the answer and working
Answer: 108 cm²
Two triangles: 2 × 3 × 4 ÷ 2 = 12; three rectangles: (3 + 4 + 5) × 8 = 96; in all 108.
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