Area of a Triangle Calculator

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