Surface Area of Solids

Q: How do you work out the surface area of a solid?

Work out the area of each face of the solid, then add all the face areas together. That total is the surface area. You measure it in square units, such as square centimetres (cm²), because every face is a flat surface. Make sure you include every face, leaving none out.

Q: How do you find the surface area of a cuboid?

A cuboid has six faces arranged in three matching pairs. Work out each pair: 2 times length times width, 2 times length times height, and 2 times width times height. Add the three pair areas together to find the surface area. Because each pair shares the same area, you simply double it.

Q: What is the formula for the surface area of a cube?

The formula is 6 × a², where a is the length of one edge. A cube has six identical square faces, and the area of one face is a × a, or a². Because all six faces are the same, you multiply one face's area by six to get the total surface area.

Q: How do you find the surface area of a triangular prism?

A triangular prism has five faces: two identical triangles and three rectangles. Work out each triangle with one half times base times height. Work out each rectangle with length times width. Add all five face areas together, and the total is the surface area of the prism.

Q: What units is surface area measured in?

Surface area is always measured in square units, because each face is a flat region with its own area. Every worked example on this page uses lengths in centimetres, so each surface area is given in square centimetres (cm²). The squared unit shows you have measured an area.

Key concept

Surface area is the total area of all the faces of a 3D shape. A cube has 6 identical square faces, so its surface area is 6 × a × a, while a cuboid has 6 faces in 3 matching pairs, giving 2lw + 2lh + 2hw.

Surface Area of Solids - introduction visual

Video Lesson

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$Surface Area of Solids poster$

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Flashcards

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Surface area calculation of a cuboid with labelled dimensions: length (l), width (w), and height (h). Illustration highlights 6 faces in 3 pairs.

Illustration showing surface area formulas for a cuboid and a cube. The cuboid formula is 2lw + 2lh + 2hw, and the cube formula is 6a².

Diagram illustrating how to find the surface area of a cuboid with dimensions, by breaking down the calculations for each face and sum up.

A trapezium prism with labelled dimensions used to calculate its surface area. The faces include front and back trapeziums, base, top, and slanted side.

What is Surface Area?

Surface area is the total area of all the faces of a solid.
To find it, calculate the area of each face and add them together.

Practice Questions

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Q1Easy

What is the surface area of a cube with a side length of $4 cm$ ?

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Interactive Activity

Click on the faces to calculate surface area

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Selected Areas

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to calculate their area

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Students Also Ask

The questions students bump into most on this topic

How do you work out the surface area of a solid?

Work out the area of each face of the solid, then add all the face areas together. That total is the surface area. You measure it in square units, such as square centimetres (cm²), because every face is a flat surface. Make sure you include every face, leaving none out.

How do you find the surface area of a cuboid?

A cuboid has six faces arranged in three matching pairs. Work out each pair: 2 times length times width, 2 times length times height, and 2 times width times height. Add the three pair areas together to find the surface area. Because each pair shares the same area, you simply double it.

What is the formula for the surface area of a cube?

The formula is 6 × a², where a is the length of one edge. A cube has six identical square faces, and the area of one face is a × a, or a². Because all six faces are the same, you multiply one face's area by six to get the total surface area.

How do you find the surface area of a triangular prism?

A triangular prism has five faces: two identical triangles and three rectangles. Work out each triangle with one half times base times height. Work out each rectangle with length times width. Add all five face areas together, and the total is the surface area of the prism.

What units is surface area measured in?

Surface area is always measured in square units, because each face is a flat region with its own area. Every worked example on this page uses lengths in centimetres, so each surface area is given in square centimetres (cm²). The squared unit shows you have measured an area.

What is the difference between a cube and a cuboid?

A cube is a special type of cuboid. A cuboid has six rectangular faces in three matching pairs, and the pairs can be different sizes. A cube is a cuboid where every edge is the same length, so all six faces are identical squares. This is why a cube uses the simpler formula 6 × a².

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