Area of triangles and parallelograms
A clear starting point, worked steps and space to practise.
Start here
Extension: these area formulas go beyond the formula work specified at this level in Victorian Curriculum Version 2.0. This is a Pi Leo topic grouping, not a statement of official year-level coverage.
A triangle is half of a parallelogram with the same base and perpendicular height.
The sloping side is not usually the height. Look for the perpendicular distance to the base.
1 Work through these steps
- Choose a base.
- Find the height at a right angle to that base.
- For a triangle, calculate base × height ÷ 2.
- For a parallelogram, calculate base × height; use square units.
2 Follow a worked example
Find the area of a triangle with base 8 cm and perpendicular height 5 cm.
- The matching parallelogram has area 8 × 5 = 40 cm².
- The triangle is half of it.
- 40 ÷ 2 = 20 cm².
3 Try it yourself
Show each step on paper or open Working out. Then check the answer.
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A parallelogram has base 9 m and perpendicular height 4 m. Find its area.
Check answer 1
Answer: 36 m²
9 × 4 = 36; do not halve for a parallelogram.
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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 triangle is half of a parallelogram with the same base and perpendicular height.
- The sloping side is not usually the height. Look for the perpendicular distance to the base.
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.
- Encourage a quick diagram or table for word problems before calculating.
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.