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What is triangle area?

Triangle area measures the flat surface enclosed by three sides. Along with the rectangle, it's the most widely used shape in architecture, carpentry, civil engineering, and graphic design. Any polygon can be broken down into triangles, making this calculation the foundation of all surface geometry.

Triangle area formulas

Main formula (base and height):
Area = (base × height) / 2

If you know all three sides (Heron's formula):
Semi-perimeter s = (a + b + c) / 2
Area = √(s × (s-a) × (s-b) × (s-c))

If you know two sides and the angle between them:
Area = (a × b × sin(θ)) / 2

Step-by-step examples

Calculate the area of a triangular roof section 9 m wide and 4 m tall.

1. Area = (9 × 4) / 2 = 18 m²
2. Add 10% waste for roofing tiles: 18 × 1.10 = 19.8 m² of material needed

Heron's formula: Triangle with sides 7, 8, and 9 m.

1. s = (7+8+9)/2 = 12
2. Area = √(12 × 5 × 4 × 3) = √720 ≈ 26.83 m²

Practical applications

• Gabled roofs: Calculate exact area of each triangular roof panel for tiles, waterproofing, or solar panels.
• Irregular plots: Divide the land into triangles, sum their areas to get total surface area.
• Carpentry and woodworking: Calculate material needed for triangular pieces with minimal waste.
• Graphic design and architecture: Triangular elements are everywhere in logos, facades, and structures.
• Applied trigonometry: Foundation for calculating forces, vectors, and stresses in structures.

How to measure a triangle's height

The height of a triangle is the perpendicular distance from the base to the opposite vertex. In a right triangle, the height relative to the hypotenuse is h = (leg₁ × leg₂) / hypotenuse. In obtuse triangles, the height falls outside the triangle — extend the base line to measure it correctly.