The area of a triangle measures the two-dimensional space enclosed by three sides. There are four main methods to calculate it.
Method 1: Base × Height
A = ½ × b × h
Example: b = 10 cm, h = 6 cm → A = 30 cm²
Method 2: Heron's Formula
A = √[s(s−a)(s−b)(s−c)]
s = (a+b+c)/2
s = (a+b+c)/2
Example: sides 7, 8, 9 → s = 12 → A = √720 = 26.83 cm²
Method 3: SAS (½ab sin C)
A = ½ × a × b × sin(C)
Example: a = 5, b = 7, C = 60° → A = 15.16 cm²
Method 4: Coordinate Formula
A = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
When to Use Which
| Known | Method |
|---|---|
| Base + height | ½bh |
| 3 sides | Heron |
| 2 sides + angle | SAS |
| Coordinates | Coordinate |
Common Mistakes
- Using slant height instead of perpendicular height
- Forgetting the ½ factor
- Calculator in wrong angle mode for sin()
Related
Triangle Area Calculator | Triangular Prism | Pyramid | Area Formulas | How to Calculate Area