Triangle Calculator

Calculate area, perimeter, and triangle type from three sides

Understanding Triangles

A triangle is a polygon with three sides and three angles. The sum of all interior angles in any triangle is always 180 degrees. This calculator uses the three side lengths to determine the triangle's properties using Heron's Formula.

ABCabc

A triangle with sides a, b, and c

Heron's Formula

Heron's formula calculates the area of a triangle when you know all three side lengths:

Step 1: Calculate semi-perimeter (s)
s = (a + b + c) / 2
Step 2: Calculate area
Area = √[s(s-a)(s-b)(s-c)]
Example: Triangle with sides 3, 4, 5
s = (3 + 4 + 5) / 2 = 6
Area = √[6(6-3)(6-4)(6-5)]
Area = √[6 × 3 × 2 × 1]
Area = √36 = 6 square units

Triangle Types

555
Equilateral
All three sides equal
Example: 5, 5, 5
556
Isosceles
Two sides equal
Example: 5, 5, 6
678
Scalene
All sides different
Example: 6, 7, 8

Practical Examples

🏗️ Construction & Architecture

Calculate roof dimensions, support beam angles, and triangular structural elements

📐 Land Surveying

Determine property boundaries and plot areas using triangulation measurements

🎨 Design & Graphics

Create precise triangular shapes and calculate dimensions for logos and artwork

📚 Education

Learn and verify geometry problems, understand triangle properties and theorems

Triangle Inequality Theorem

For any triangle to be valid, the sum of any two sides must be greater than the third side:

a + b > c
b + c > a
a + c > b
✓ Valid Triangle
Sides: 3, 4, 5
3 + 4 = 7 > 5 ✓
4 + 5 = 9 > 3 ✓
3 + 5 = 8 > 4 ✓
✗ Invalid Triangle
Sides: 1, 2, 5
1 + 2 = 3 < 5 ✗
Cannot form a triangle!

💡 Quick Tips

  • Right Triangles: If a² + b² = c², it's a right triangle (Pythagorean theorem)
  • Perimeter: Simply add all three sides together (a + b + c)
  • Units: Ensure all sides use the same unit of measurement
  • Equilateral Area: Can also use formula: Area = (√3/4) × side²