Every triangle is half of a rectangle (or parallelogram) with the same base and height. So the area is ½ × base × height. The height must be at right angles to the base: it is the straight-up distance, often drawn as a dashed line. Never use a slanted side as the height. In an obtuse triangle, the height falls outside the shape and the base is extended with a dashed line, but the extension is not part of the base.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- base
- the side the triangle sits on
- perpendicular height
- the distance from the base to the top corner, measured at a right angle
- obtuse triangle
- a triangle with one angle bigger than a right angle
Worked examples
A triangle has a base of 8 cm and a height of 5 cm. What is its area?
- 1.Area = ½ × base × height.
- 2.½ × 8 × 5 = ½ × 40 = 20 cm².
= 20
A triangle has a base of 10 cm, a dashed height of 6 cm and a slanted side of 8 cm. What is its area?
- 1.Use the dashed height, not the slanted side.
- 2.½ × 10 × 6 = ½ × 60 = 30 cm².
= 30
An obtuse triangle has a base of 6 cm, a height of 4 cm outside it and a dashed extension of 3 cm. What is its area?
- 1.The extension is not part of the base.
- 2.½ × 6 × 4 = ½ × 24 = 12 cm².
= 12
For parents
Method: Half of base times height
What to say: Which line meets the base at a right angle? Did you halve?
Common mistakes:
- Multiplies base by height but forgets to halve, giving the area of the surrounding rectangle.
- Uses a slanted side as the height instead of the perpendicular height.
- Adds the base and height instead of multiplying.
- In an obtuse triangle, adds the dashed extension to the base.