Surface Area
Surface area is the total area of every face of a 3D shape added together, measured in square units such as cm^2 or m^2. It is a key GCSE Geometry and Measures topic, testing whether you can identify all the faces of solids like cuboids, prisms, cylinders and spheres, then add their areas correctly.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify every face of the solid and what shape each face is (rectangle, triangle, circle, and so on).
- Work out the area of each different face using the correct 2D area formula.
- Multiply by how many faces share that area, for example two identical triangular ends.
- Add all the face areas together to get the total surface area.
- Check the units are squared (cm^2, m^2) and round only the final answer if asked.
- For curved surfaces on cylinders, cones and spheres, use the given formula rather than trying to unfold it yourself.
Worked example
A triangular prism has a right-angled triangular cross-section with shorter sides 6 cm and 8 cm and hypotenuse 10 cm. The prism is 15 cm long. Work out the total surface area of the prism.
- The two triangular ends: area = 0.5 x 6 x 8 = 24 cm^2 each, so 48 cm^2 for both.
- The three rectangular faces: 6 x 15 = 90 cm^2, 8 x 15 = 120 cm^2, 10 x 15 = 150 cm^2.
- Add the rectangles: 90 + 120 + 150 = 360 cm^2.
- Total surface area = 48 + 360.
- Final answer: 408 cm^2.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A cube has volume 125 cm^3. Work out the total surface area of the cube.
A closed cylinder has radius 5 cm and height 9 cm. Work out the total surface area of the cylinder. Give your answer correct to 3 significant figures.
An isosceles triangular prism has a cross-section with base 8 cm and two equal sides of 5 cm. The prism has length 14 cm. (a) Show that the perpendicular height of the triangular cross-section is 3 cm. (b) Work out the total surface area of the prism.
See real past-paper questions on surface area, organised by topic with official mark schemes →
Free printable worksheet
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