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CalcSolver

Triangle Calculator (Area & Perimeter)

Enter the three side lengths to find the area (via Heron’s formula), the perimeter, the semi-perimeter and the triangle type. The calculator also checks that the sides form a valid triangle.

CalculatorEnter values below

Formula

Area = √(s(s−a)(s−b)(s−c)), where s = (a + b + c) ÷ 2 (Heron’s formula)

How it works

  1. 1

    First the calculator checks the triangle inequality: the sum of any two sides must exceed the third.

  2. 2

    The semi-perimeter s is half of the perimeter (a + b + c).

  3. 3

    Heron’s formula then gives the area directly from the three side lengths.

  4. 4

    The triangle is also classified by its sides (scalene, isosceles, equilateral) and angles (acute, right, obtuse).

Worked examples

A 3–4–5 right triangle

Find the area of a triangle with sides 3, 4 and 5.

  1. Perimeter = 3 + 4 + 5 = 12, so s = 6
  2. Area = √(6 × 3 × 2 × 1) = √36 = 6
  3. Since 3² + 4² = 5², it is a right triangle.

Answer: Area = 6

Equilateral triangle

Find the area of a triangle with sides 6, 6 and 6.

  1. s = 18 ÷ 2 = 9
  2. Area = √(9 × 3 × 3 × 3) = √243 ≈ 15.588

Answer: Area ≈ 15.59

Frequently asked questions

How do you find the area of a triangle from three sides?
Use Heron’s formula. Compute the semi-perimeter s = (a + b + c) ÷ 2, then Area = √(s(s−a)(s−b)(s−c)).
What is the triangle inequality?
For three lengths to form a triangle, the sum of any two sides must be greater than the third side. If not, no triangle exists.
How is a triangle classified?
By sides: equilateral (all equal), isosceles (two equal) or scalene (all different). By angles: acute, right (one 90° angle) or obtuse.
What is the perimeter of a triangle?
The perimeter is simply the sum of all three side lengths: a + b + c. The semi-perimeter, used in Heron’s formula, is half of that.
Do I need the height to find the area?
No. This calculator uses Heron’s formula, which finds the area directly from the three side lengths — no height or angle is required.
Why do my three sides say “not a valid triangle”?
They fail the triangle inequality — the two shorter sides don’t add up to more than the longest side, so they can’t close into a triangle (for example 2, 3 and 10).