Area of a Triangle Calculator
Calculate triangle area using multiple methods: base & height, Heron's formula, SAS, and more. Step-by-step solutions with visual diagrams.
Triangle Area Calculator
Triangle Area Formulas
Base & Height: A = (b × h) ÷ 2
Heron's Formula: A = √[s(s-a)(s-b)(s-c)]
SAS Method: A = (1/2) × a × b × sin(C)
Right Triangle: A = (leg₁ × leg₂) ÷ 2
Triangle Types
Equilateral: All sides equal, all angles 60°
Area = (√3/4) × side²
Area = (√3/4) × side²
Isosceles: Two sides equal, two angles equal
Has line of symmetry through apex
Has line of symmetry through apex
Scalene: All sides different, all angles different
No lines of symmetry
No lines of symmetry
Right Triangle: One 90° angle
Area = (leg₁ × leg₂) ÷ 2
Area = (leg₁ × leg₂) ÷ 2
Understanding Triangle Area Calculations
Calculating the area of a triangle is a fundamental concept in geometry with numerous real-world applications. There are several methods available depending on what information you have about the triangle.
Method Selection Guide:
- Base and Height: Use when you know one side and the perpendicular height to that side
- Heron's Formula: Use when you know all three side lengths
- SAS Method: Use when you know two sides and the included angle
- Coordinate Method: Use when you have the coordinates of all three vertices
Triangle Properties:
- Triangle Inequality: Sum of any two sides must be greater than the third
- Angle Sum: All interior angles sum to 180°
- Area Relationship: Area is always positive and depends on side lengths and angles
- Similarity: Similar triangles have proportional sides and equal angles
Real-World Applications:
- Architecture: Calculating roof areas and triangular structural elements
- Surveying: Measuring land areas and property boundaries
- Engineering: Stress analysis in triangular trusses and frameworks
- Computer Graphics: Rendering triangular surfaces in 3D models
- Navigation: Triangulation for GPS and mapping systems
Frequently Asked Questions - Triangle Area Calculator
There are several methods: 1) Base and Height (A = bh/2), 2) Heron's Formula using three sides, 3) SAS using two sides and included angle, and 4) Coordinate geometry using vertex coordinates.