Triangle Area Calculator
Choose the measurements you have. The calculator finds the area, and for three known sides also the perimeter, angles and heights.
Result
Formula
- Area = ½ × base × height
- Heron: Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) ÷ 2
- Two sides and included angle: Area = ½ × a × b × sin(C)
- Law of cosines: c² = a² + b² − 2ab × cos(C)
How the Triangle Area Calculator works
The area of any triangle is half the base times the perpendicular height. When the height is not known, Heron's formula gives the area from the three side lengths alone, using the semi-perimeter s.
If you know two sides and the angle between them, the height is one side times the sine of the angle, which leads to the third formula.
Worked example
A triangle with a base of 10 cm and a height of 6 cm has an area of ½ × 10 × 6 = 30 cm². With sides 7, 8 and 9, s = 12 and the area is √(12 × 5 × 4 × 3) = √720 = 26.8328.
Frequently asked questions
How do I find the area of a triangle without the height?
Use Heron's formula with the three sides, or ½ × a × b × sin(C) if you know two sides and the angle between them.
What is the area of an equilateral triangle?
Area = (√3 ÷ 4) × side². For a side of 6 it is 15.588.
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