Triangle Area Calculator
Calculate triangle area using base & height, Heron's formula, SAS, or ASA methods
Calculate Triangle Area
Most basic formula using base and height
Length of the triangle base
Perpendicular height to base
Triangle Area Results
Base and height must be positive numbers
Example Calculations
Base and Height Method
Given: Base = 10 units, Height = 6 units
Formula: Area = ½ × base × height
Calculation: Area = ½ × 10 × 6 = 30 square units
Heron's Formula Method
Given: Sides = 3, 4, 5 units
Semiperimeter: s = (3 + 4 + 5) / 2 = 6
Formula: Area = √[s(s-a)(s-b)(s-c)]
Calculation: Area = √[6 × 3 × 2 × 1] = √36 = 6 square units
Triangle Area Formulas
Base & Height
Area = ½ × b × h
Most basic formula
Heron's Formula
Area = √[s(s-a)(s-b)(s-c)]
When all sides are known
SAS Formula
Area = ½ × a × b × sin(C)
Two sides + included angle
ASA Formula
Area = a² × sin(B) × sin(C) / (2 × sin(A))
Two angles + included side
Area Tips
Base × Height is the simplest method when height is known
Use Heron's formula when only side lengths are known
SAS method works well with two sides and included angle
For equilateral triangles: Area = (√3/4) × side²
Understanding Triangle Area Calculations
Different Calculation Methods
1. Base and Height (Most Common)
The fundamental formula: Area = ½ × base × height. Works when you know the base and the perpendicular height to that base.
2. Heron's Formula (Three Sides)
Uses all three side lengths. First calculate the semiperimeter, then apply the square root formula.
3. SAS Method (Two Sides + Angle)
When you know two sides and the angle between them. Uses trigonometry with the sine function.
4. ASA Method (Two Angles + Side)
When you know two angles and the side between them. More complex but very accurate.
Special Triangle Cases
Right Triangle
Area = ½ × leg₁ × leg₂ (legs are perpendicular)
Equilateral Triangle
Area = (√3/4) × side² ≈ 0.433 × side²
Isosceles Triangle
Can use base & height or any other method depending on known values