Triangle Area (Heron's Formula)
Enter the three sides a, b and c to compute the area of a triangle with Heron's formula. It also shows the perimeter and semi perimeter s, and draws the triangle to scale.
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Input
Enter the three sides a, b and c of a triangle to find its area using Heron''s formula.
Result
Area
6
Perimeter
12
Semi perimeter s
6
The length unit matches the input values and the area is in the squared unit.
How it works
- The semi perimeter s is computed as s equals (a plus b plus c) divided by 2.
- The area uses Heron's formula, the square root of s times (s minus a) times (s minus b) times (s minus c).
- The three sides must be positive and the sum of any two sides must be greater than the remaining side for a valid triangle.
- The length unit matches the input values and the area is in the squared unit.
Frequently asked questions
- How does Heron's formula compute the area?
- It first finds the semi-perimeter s = (a + b + c) ÷ 2, then computes area = √(s(s − a)(s − b)(s − c)). This lets you find the area from the three sides alone, with no height needed.
- How is this different from the base-and-height triangle tool?
- This tool uses the three sides a, b and c via Heron's formula, so you never need the height. If you already know the base and its perpendicular height, the base × height ÷ 2 tool is simpler—pick the one that matches the values you have.
- Do any three side lengths work?
- All three sides must be positive, and the sum of any two sides must be greater than the third for a triangle to exist. Values that break this triangle inequality cannot form a triangle and won't compute.
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