Area of composite shapes
A clear starting point, worked steps and space to practise.
Start here
A composite shape can be split into shapes with area rules you already know.
Choose the split that needs the fewest missing lengths. Label each region before calculating.
1 Work through these steps
- Mark a split into rectangles or triangles.
- Find any missing lengths.
- Calculate each area.
- Add separate pieces, or subtract a cut-out, without counting any area twice.
2 Follow a worked example
A 10 m by 6 m rectangle has a 3 m by 2 m rectangle cut out of one corner. What area remains?
- Whole rectangle: 10 × 6 = 60 m².
- Cut-out: 3 × 2 = 6 m².
- Remaining area: 60 − 6 = 54 m².
3 Try it yourself
Show each step on paper or open Working out. Then check the answer.
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An 8 cm by 5 cm rectangle has a 2 cm by 2 cm corner removed. Find the remaining area.
Check answer 1
Answer: 36 cm²
8 × 5 − 2 × 2 = 40 − 4 = 36 cm².
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Working out
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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
- A composite shape can be split into shapes with area rules you already know.
- Choose the split that needs the fewest missing lengths. Label each region before calculating.
Method and checking
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.