Quick answer: for any triangle with three known sides, use Heron's formula for area. For right triangles, use the Pythagorean theorem to find a missing side. Try our free Triangle Calculator.
Heron's Formula
Given sides a, b, c: first find the semi-perimeter s = (a+b+c)/2, then Area = √(s(s-a)(s-b)(s-c)). This works for any triangle, not just right triangles.
Pythagorean Theorem
For right triangles: a² + b² = c², where c is the hypotenuse. Knowing any two sides lets you solve for the third.
Frequently Asked Questions
Does Heron's formula work for right triangles too?
Yes, it works for any triangle type, including right triangles.
What if I only know two sides and an angle?
The calculator can also solve using the Law of Cosines when an angle is known instead of the third side.
Can this calculate perimeter too?
Yes, perimeter is simply the sum of all three sides.
✨ Try it now — free & instant
Open the Tool →Worked example with the base and height
Suppose a triangle has a base of 10 cm and a perpendicular height of 6 cm. Its area is ½ × 10 × 6 = 30 cm². The height must meet the base at a right angle; a sloping side is not automatically the height. If the triangle is right-angled, the two sides that form the right angle can be used as base and height.
Using three sides instead
When all three side lengths are known, first find the semiperimeter: s = (a + b + c) ÷ 2. Heron’s formula then gives the area: √[s(s−a)(s−b)(s−c)]. For sides 5, 5, and 6 cm, s = 8, so the area is √(8×3×3×2) = 12 cm².
Before calculating, check the triangle inequality: the sum of any two side lengths must be greater than the third. A set of 2, 3, and 6 cannot make a triangle. Keep units consistent, and express area in square units (cm², m²), while perimeter is a length (cm, m). These formulas assume a flat, ordinary Euclidean triangle.
Choose the formula from the measurements
Use ½bh when you have a base and its perpendicular height. Use Heron’s formula when all three sides are known. If you have two sides and the included angle, the area can also be found with ½ab sin(C). Do not mix a side length with a non-perpendicular altitude. When solving for a missing side, identify whether the triangle is right-angled; Pythagoras applies only in that case. Rounding too early can create a noticeable difference in small triangles, so keep extra decimal places until the final result.