Triangle Area Calculator
Use base and height, or switch to three sides for Heron's formula — instant either way.
Two Ways to Find Triangle Area
If you know the base and the perpendicular height, area = (1/2) × base × height. If you only know the three side lengths, Heron's formula gets there without ever needing a height.
Worked example (Heron's formula)
A triangle with sides 5, 6, and 7.
Semi-perimeter s = (5 + 6 + 7) / 2 = 9
Area = √(9 × (9−5) × (9−6) × (9−7)) = √(9 × 4 × 3 × 2) = √216 ≈ 14.70
Frequently Asked Questions
What is the formula for the area of a triangle?
Area = (1/2) × base × height, when you know the base and the perpendicular height. If you only know the three side lengths, use Heron's formula instead.
What is Heron's formula?
Heron's formula finds a triangle's area from its three side lengths a, b, c alone, with no height needed: first find the semi-perimeter s = (a + b + c) / 2, then area = √(s(s − a)(s − b)(s − c)).
Why does the calculator say three side lengths can't form a triangle?
The triangle inequality requires each side to be shorter than the sum of the other two. If one side is too long relative to the others, no triangle can actually close up — for example, 2, 3, and 10 can never form a triangle.
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