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.
Formula
Area = √(s(s−a)(s−b)(s−c)), where s = (a + b + c) ÷ 2 (Heron’s formula)
How it works
- 1
First the calculator checks the triangle inequality: the sum of any two sides must exceed the third.
- 2
The semi-perimeter s is half of the perimeter (a + b + c).
- 3
Heron’s formula then gives the area directly from the three side lengths.
- 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.
- Perimeter = 3 + 4 + 5 = 12, so s = 6
- Area = √(6 × 3 × 2 × 1) = √36 = 6
- 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.
- s = 18 ÷ 2 = 9
- 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.