Triangle Area Calculator
Finds the area of a triangle from its base and height.
Recent
Formula
How the calculation works
A triangle's area is half the area of a rectangle with the same base and height, so the calculation multiplies those two lengths and divides the product by two.
The base is any side you choose as the bottom reference, and the height is the perpendicular distance from that base to the opposite corner, not the length of a slanted side.
With a base of 12 and a height of 8 the product is 96, and halving it gives an area of 48 square units inside the triangle.
Common mistakes
- Do not use a slanted side as the height, because the formula needs the perpendicular distance from the base to the opposite corner and a tilted edge gives too large an area.
- The base and height must share the same unit, since mixing centimetres for one and metres for the other multiplies the error and ruins the square-unit area.
- Remember to halve the product, as forgetting the division by two is the single most common mistake and doubles the triangle's area.
When to use it
- Use it to work out the material needed for a triangular sail, gable or plot of land once you know a base and the perpendicular height.
- Use it in school geometry to find the triangle's area without needing Heron's formula, as long as a base and its matching height are known.
Worked example
A triangle with a base of 12 and a height of 8 has an area of 48 square units.
Common questions
Which side do I use as the base?
Any side can be the base, but you must pair it with the perpendicular height measured from that side to the opposite corner.
Does this work for any triangle?
Yes. As long as you know a base and the perpendicular height to the opposite corner, the half base times height rule works for every triangle shape.
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