Area of a Triangle
Area of a triangle from base and height.
Formula
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Example
A triangle with base 10 and height 4 has area A = ½·10·4 = 20.
How it works
This formula finds the area of a triangle by taking half of a rectangle or parallelogram with the same base and perpendicular height. The base is one side you choose, and the height must be the straight-up distance to that base, not the length of a slanted side. Because two congruent triangles can fit together to make a rectangle or parallelogram, a single triangle covers exactly half of that shape's area.
When to use it
Use this when you know a triangle's base and its perpendicular height, such as in geometry problems, land measurements, or design work. It is especially useful when the triangle is not a right triangle and you cannot use side lengths alone.
Worked example, step by step
A triangle has base 12 cm and height 7 cm. Use A = 1/2 b h A = 1/2 × 12 × 7 A = 6 × 7 A = 42 The area is 42 cm².
Common mistakes to avoid
- Using a slanted side as the height instead of the perpendicular height
- Forgetting to multiply by 1/2, which gives the area of a rectangle-like shape instead
- Leaving the answer in linear units instead of square units
Did You Know?
Half base times height works for ANY triangle — slant or right, the formula never changes.
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