Area of a Triangle Calculator
Find the area of any triangle using the method that matches the information you have. This calculator supports base and height, Heron's formula (three sides), and the SAS formula (two sides and an included angle).
There are several ways to calculate the area of a triangle depending on which measurements you know.
Method 1: Base and Height
A = (1/2) x base x height
This is the simplest approach when you know the base and the perpendicular height. For a triangle with base 10 and height 6, the area is (1/2)(10)(6) = 30 square units.
Method 2: Heron's Formula (Three Sides)
When you know all three side lengths a, b, and c:
- Compute the semi-perimeter: s = (a + b + c) / 2
- Area = sqrt(s(s-a)(s-b)(s-c))
For a triangle with sides 3, 4, and 5: s = 6, area = sqrt(6 x 3 x 2 x 1) = sqrt(36) = 6 square units.
Method 3: SAS (Two Sides and Included Angle)
A = (1/2) x a x b x sin(C)
where C is the angle between sides a and b. For sides 8 and 5 with a 60-degree included angle: A = (1/2)(8)(5)(sin 60°) = 20(0.866) = 17.32 square units.
All three methods produce the same result when applied to the same triangle. Pick whichever matches the data you have.