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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

a = 3b = 4c = 5

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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