Find the total area of every face of a solid — cuboids, prisms and open boxes — by listing the faces and adding their areas. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page.
Surface area is the total area of every face, as if you unfolded the net. A cuboid has three pairs of faces: 2(lw+lh+wh). A triangular prism is two triangular ends plus three rectangular sides. Draw the net or list the faces so you do not count one twice and miss another.
Units are cm². If a face is a triangle, use 21bh. A question that gives a volume as well is usually two separate demands — do not feed the volume into the surface-area formula.
Add the area of every face. A cuboid is 2(lw+lh+wh); a cube is 6a2. Nets are the same faces laid flat — do not count a face twice. Working backwards: cube surface 150 cm² → one face 25 cm² → edge 5 cm.
Objectives
Surface area adds the areas of the faces.
The three different faces are length × width, width × height, and height × length.
A net is the solid folded out flat.
Key points
List every face of a solid and its dimensions before working out any areas.
Find the surface area of a cuboid using pairs of identical faces.
Find the surface area of a triangular prism (two triangles plus three rectangles).
Adjust for open-topped or 'painted' solids where some faces are left out.
Worked examples
Example 1
A cube has sides of length 2 cm. What is its total surface area in cm²?
2 marks
One face has area 2 × 2 = 4 cm².
A cube has 6 faces.
6 × 4 = 24 cm².
Answer: 24
Common slips
Slip: One face has area 4 × 2 = 4 cm². That changes a number from the question, so it answers a different question.
Slip: A cube has 9 faces. That changes a number in the working, so the step no longer follows from the one before.
Slip: 10 × 4 = 24 cm². That does not match the working above it.
Example 2
A cuboid is 6 cm by 2 cm by 9 cm. What is its surface area in cm²?
3 marks
The three different faces are 6 × 2 = 12, 2 × 9 = 18 and 9 × 6 = 54.
Add them: 12 + 18 + 54 = 84.
Double it: 2 × 84 = 168 cm².
Answer: 168
Common slips
Slip: The three different faces are 8 × 2 = 12, 2 × 9 = 18 and 9 × 6 = 54. That changes a number from the question, so it answers a different question.
Slip: Add them: 15 + 18 + 54 = 84. That changes a number in the working, so the step no longer follows from the one before.
Slip: Double it: 6 × 84 = 168 cm². That does not match the working above it.
Example 3
A triangular prism has a right-angled triangle for its end. The triangle has sides 5 cm, 12 cm and 13 cm. The prism is 6 cm long. What is its total surface area in cm²?
4 marks
Two triangular ends: 2 × ½ × 5 × 12 = 60 cm².
Three rectangles: (5 + 12 + 13) × 6 = 180 cm².
Total = 60 + 180 = 240 cm².
Answer: 240
Common slips
Slip: Two triangular ends: 4 × ½ × 5 × 12 = 60 cm². That changes a number from the question, so it answers a different question.
Slip: Three rectangles: (8 + 12 + 13) × 6 = 180 cm². That changes a number in the working, so the step no longer follows from the one before.
Slip: Total = 64 + 180 = 240 cm². That does not match the working above it.
Questions and answers
GCSE Maths surface area questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A cuboid is 2 cm by 6 cm by 3 cm. What is its surface area in cm²?
Show answer
Answer: 72
The three different faces are 2 × 6 = 12, 6 × 3 = 18 and 3 × 2 = 6.
Add them: 12 + 18 + 6 = 36.
M1 — The three different faces are 2 × 6 = 12, 6 × 3 = 18 and 3 × 2 = 6.
A1 — Answer 72
Question 2 Easy2 marks
A cube has sides of length 11 cm. What is its total surface area in cm²?
Show answer
Answer: 726
One face has area 11 × 11 = 121 cm².
A cube has 6 faces.
M1 — One face has area 11 × 11 = 121 cm².
A1 — Answer 726
Question 3 Medium2 marks
A cube has sides of length 4 cm. What is its total surface area in cm²?
Show answer
Answer: 96
One face has area 4 × 4 = 16 cm².
A cube has 6 faces.
M1 — One face has area 4 × 4 = 16 cm².
A1 — Answer 96
Question 4 Medium2 marks
A triangular prism has a right-angled triangle for its end. The triangle has sides 6 cm, 8 cm and 10 cm. The prism is 11 cm long. What is its total surface area in cm²?
Show answer
Answer: 312
Two triangular ends: 2 × ½ × 6 × 8 = 48 cm².
Three rectangles: (6 + 8 + 10) × 11 = 264 cm².
M1 — Two triangular ends: 2 × ½ × 6 × 8 = 48 cm².
A1 — Answer 312
Question 5 Hard2 marks
A triangular prism has a right-angled triangle for its end. The triangle has sides 8 cm, 15 cm and 17 cm. The prism is 10 cm long. What is its total surface area in cm²?
Show answer
Answer: 520
Two triangular ends: 2 × ½ × 8 × 15 = 120 cm².
Three rectangles: (8 + 15 + 17) × 10 = 400 cm².
M1 — Two triangular ends: 2 × ½ × 8 × 15 = 120 cm².
A1 — Answer 520
Question 6 Hard2 marks
A cuboid is 5 cm by 7 cm by 8 cm. What is its surface area in cm²?
Show answer
Answer: 262
The three different faces are 5 × 7 = 35, 7 × 8 = 56 and 8 × 5 = 40.
Add them: 35 + 56 + 40 = 131.
M1 — The three different faces are 5 × 7 = 35, 7 × 8 = 56 and 8 × 5 = 40.
A1 — Answer 262
Question 7 Exam-style3 marks
A cuboid is 3 cm by 6 cm by 9 cm. What is its surface area in cm²?
Show answer
Answer: 198
The three different faces are 3 × 6 = 18, 6 × 9 = 54 and 9 × 3 = 27.
Add them: 18 + 54 + 27 = 99.
Double it: 2 × 99 = 198 cm².
M1 — The three different faces are 3 × 6 = 18, 6 × 9 = 54 and 9 × 3 = 27.
M1 — Double it: 2 × 99 = 198 cm².
A1 — Answer 198
Common mistakes
Most lost marks on this topic are one slip.
Finding the volume instead of the surface area.
Volume multiplies three lengths once. Surface area adds the faces.
Forgetting to double the three faces.
Each face has an opposite partner.
Missing the ends of a prism.
There are two ends as well as the rectangular sides.
Spot the slip
A cuboid has how many faces?
6
4
8
Show the slip
6 Three pairs: front and back, left and right, top and bottom.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
List faces with their areas one per line; a full correct list earns method marks even if the final addition slips.
Write cm² (not cm or cm³) — wrong units can cost the accuracy mark.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.