Surface area of composite solids
A clear starting point, worked steps and space to practise.
Start here
For joined solids, surface area includes only the faces exposed on the outside.
For a shared face, subtract twice its area from the sum of the separate surface areas.
1 Work through these steps
- List the surface areas before joining.
- Identify the shared faces.
- Remove each hidden shared face from both solids.
- Add the remaining exposed areas.
2 Follow a worked example
Two cubes with edge 2 cm are joined along one complete face. Find the surface area of the resulting solid.
- Each cube has area 6 × 2² = 24 cm².
- Together before joining: 48 cm².
- Two 4 cm² faces become hidden.
- Exposed area = 48 − 8 = 40 cm².
3 Try it yourself
Show each step on paper or open Working out. Then check the answer.
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Two cubes of edge 3 cm are joined along one full face. Find the exposed surface area.
Check answer 1
Answer: 90 cm²
2 × 54 − 2 × 9 = 108 − 18 = 90 cm².
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Check your understanding
Explain the worked example in your own words. Say why the method works, not just what the answer is.
Skills and explanation links
Key ideas taught here
- For joined solids, surface area includes only the faces exposed on the outside.
- For a shared face, subtract twice its area from the sum of the separate surface areas.
Method and checking
Optional recap: related Maths skills
These earlier examples revisit background skills. Start with the topic example and practice above.
Useful vocabulary
- area
- The space inside a flat shape.
- perimeter
- The distance around a shape.
- square unit
- A unit used to measure area.
- formula
- A rule used to calculate efficiently.
Rules for these related skills
Area measures inside space; perimeter measures around the edge.
Area of a rectangle = length x width.
Area uses square units such as square cm or square m.
Find the perimeter of a 5 cm by 3 cm rectangle.
- Perimeter is around the outside.
- 5 + 3 + 5 + 3 = 16.
- Answer: 16 cm.
Find the area of a 6 m by 4 m rectangle.
- Area = length x width.
- 6 x 4 = 24.
- Answer: 24 square metres.
Find the area of a triangle with base 8 cm and height 5 cm.
- Triangle area = base x height / 2.
- 8 x 5 = 40.
- 40 / 2 = 20 square centimetres.
A garden bed is 7 m long and 2 m wide. How much soil area is covered?
- Use area, not perimeter.
- 7 x 2 = 14.
- The area is 14 square metres.
More visual models and everyday examples
Each everyday example has its own information and model. Use its stated values rather than copying values from another question.
Concept example. The story examples below have their own diagrams.
Count one row, then multiply by the number of rows.
For parents and teachers
- Ask your child to explain the method aloud before writing the answer.
- Use a real-life context at home, such as shopping, cooking, sport scores, maps or timetables.
- Praise clear working and checking, not only speed.
- Ask your child to write the formula or rule first, then substitute values carefully.
Practise choosing a method from the information in the question. The examples here are Pi Leo Academy learning activities. Official NAPLAN testing takes place in Years 3, 5, 7 and 9; a topic appearing in these notes does not mean it is tested in NAPLAN.
These notes provide guided examples and practice; they do not certify completion of every curriculum requirement.