Triangle Calculator
Solve triangle area from base and height, or from all three sides using Heron’s formula.
Triangle Calculator
Solve triangle area from base and height, or from all three sides using Heron’s formula.
How to use the Triangle Calculator
- Choose "Base & height" or "Three sides" mode.
- Enter the measurements.
- Click Calculate.
Formula
Base & height: A = ½ × b × h
Heron's: A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
Example
Three sides 5, 12, 13: s = 15. A = √(15×10×3×2) = √900 = 30.
Step-by-step calculation
- Calculate semi-perimeter: s = (5+12+13)/2 = 15.
- Heron's formula: √(15 × 10 × 3 × 2).
- Multiply inside: 15×10×3×2 = 900.
- Square root: √900 = 30.
Real-world uses
- Land surveying.
- Structural engineering.
- Roof area calculations.
Common mistakes
- Entering sides that cannot form a triangle (must satisfy triangle inequality).
- Using base × height without the ½ multiplier.
- For Heron's formula, getting the semi-perimeter wrong.
Frequently asked questions
What is the triangle inequality?
The sum of any two sides must be greater than the third side. 5+12 > 13 is true, so it works.
What is a right triangle?
A triangle with one 90° angle. The Pythagorean theorem applies: a² + b² = c².
How do I know the triangle type from three sides?
If c² = a²+b² it is right. If c² < a²+b² it is acute. If c² > a²+b² it is obtuse.