Primary 5 maths · Measurement & time · About 12 minutes
Find the area of a triangle
Check a building block, predict, try the model, then explain and use the idea.
Start the interactive lesson →Practise: Triangle gardens
What you will learn
- Find the area of a triangle
Models used: number sentences, stories, diagrams.
Before you start
Two triangles explain the half
A blue triangle has base 6 units and perpendicular height 4 units. How much surface does it cover?
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
We want to find how much surface this blue triangle covers. Its base is 6 units and its height is 4 units.
Area measures the inside surface. The right-angle mark shows that the height is perpendicular to the base.
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
Make an identical copy of the blue triangle. Turn the copy to fill the empty half.
The orange triangle has exactly the same area as the blue one. Together they fill a rectangle, with no gap or overlap.
Each little square is one square unit. There are 6 squares across and 4 rows.
The rectangle is 6 units across and 4 units high. Its area is 24 square units.
6 × 4 = 24 square units
There are six squares in each of four equal rows. That is why we multiply the base and height.
Is 24 the area of one triangle or of both triangles together?
Both triangles together. The rectangle contains two equal copies of our triangle.
Base = 6 units. Perpendicular height = 4 units. The little square marks a right angle.
Share that area equally between the two triangles. Each triangle covers 12 square units.
triangle area = base × height ÷ 2 = 12
We divide by two because our rectangle contains two matching triangles. The formula records what the picture showed us.
What did the picture help us see?
Share that area equally between the two triangles. Each triangle covers 12 square units.
Worked example: Use the rectangle idea with less help
A triangle has base 8 units and perpendicular height 5 units. What is its area?
One blue triangle. The right-angle mark identifies its height.
The dimensions have changed to eight and five. A matching copy still completes a rectangle. First find that rectangle’s area.
Two matching triangles fill the rectangle.
What is the rectangle area in square units?
40
Forty belongs to two equal triangles. Decide how much belongs to just the blue one.
Two matching triangles fill the rectangle.
A triangle has base 8 units and perpendicular height 5 units. What is its area?
20
Base and perpendicular height match the rectangle dimensions. Area uses square units.
One triangle covers twenty square units. Doubling it gives the forty-square-unit rectangle again.
8 × 5 ÷ 2 = 20; check: 20 × 2 = 40
One blue triangle. The right-angle mark identifies its height.
Common mistakes to discuss
- Forgetting to halve. Two matching triangles fill the rectangle. With base 8 cm and height 7 cm the area is 56 ÷ 2 = 28 cm².
Check your understanding
- explain why triangle area is half of base times height
- use the perpendicular height shown in a picture
- spot and correct a missing divide-by-two step
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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