Scalene Triangle Area Calculator
Calculate the area of a scalene triangle using multiple methods: base & height, 3 sides, or angles
Calculate Scalene Triangle Area
Perpendicular distance from base to opposite vertex
Area Calculation Results
About Scalene Triangles
All three sides have different lengths
All three angles are different
Most common type of triangle
Can be acute, right, or obtuse
No lines of symmetry
Area Formulas
Base & Height
A = ½ × b × h
Heron's Formula
A = √[s(s-a)(s-b)(s-c)]
s = (a+b+c)/2
SAS Formula
A = ½ab sin(C)
ASA Formula
A = a²sin(β)sin(γ)/(2sin(β+γ))
Quick Example
Triangle with sides 3, 5, 7 inches
s = (3+5+7)/2 = 7.5
A = √[7.5×4.5×2.5×0.5]
A = √42.1875 ≈ 6.495 in²
How to Calculate Scalene Triangle Area
Method 1: Base and Height
The simplest method when you know the base and height. The height must be perpendicular to the base.
Area = ½ × base × height
Method 2: Heron's Formula
Use when you know all three sides. This ancient formula works for any triangle.
Area = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2
Method 3: SAS Formula
Use when you know two sides and the included angle between them.
Area = ½ × a × b × sin(C)
Method 4: ASA Formula
Use when you know two angles and the included side between them.
Area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))
where γ = 180° - α - β
Important Notes
For a valid triangle, the sum of any two sides must be greater than the third side
Scalene triangles have all different side lengths
The sum of all angles in any triangle is always 180°
Heron's formula is most accurate for numerical calculations
SAS method requires the angle between the two given sides
Always check units - area is in square units