Triangle Area Calculator
Calculate the area and perimeter of any triangle — using base & height or Heron's formula for three sides.
What is the Triangle Area Calculator?
The Triangle Area Calculator finds the area of any triangle using two methods: the classic base × height formula, or Heron's formula when all three sides are known. The triangle is the most fundamental polygon in geometry — it appears in architecture, engineering, navigation, physics, and countless competitive exam problems.
Method 1 — Base & Height
If you know the base and perpendicular height of the triangle: Area = ½ × base × height. This is the simplest and most commonly used formula.
Method 2 — Heron's Formula (Three Sides)
If you only know the three side lengths (without height), Heron's formula calculates the area exactly. This is especially useful for triangles drawn on paper or described by side lengths. The formula also confirms whether the three sides form a valid triangle.
Applications
- Land surveying: calculating plot areas
- Architecture: roof area, triangular floor plans
- Physics: force decomposition diagrams
- Competitive exams: CBSE, JEE, SSC mensuration problems
- Woodworking and carpentry: cutting triangular pieces
How Does the Triangle Area Calculator Work?
1. Select Mode: Choose "Base & Height" or "Three Sides (Heron's Formula)".
2. Base & Height mode: Enter the base length and perpendicular height.
3. Three Sides mode: Enter all three side lengths (a, b, c). The calculator verifies the triangle inequality.
4. View Results: Area is shown in square units. For three-sides mode, perimeter is also calculated.
Formula & Calculation Method
Base & Height: Area = ½ × b × h
Heron's Formula: Area = √(s(s−a)(s−b)(s−c))
Where s = (a + b + c) / 2 (semi-perimeter)
Triangle Inequality: a + b > c, a + c > b, b + c > a (must hold for a valid triangle)
Perimeter = a + b + c
Example Calculation
Example 1 — Base & Height: base = 10 cm, height = 6 cm → Area = ½ × 10 × 6 = 30 cm²
Example 2 — Heron's Formula: sides 13, 14, 15 cm → s = 21; Area = √(21×8×7×6) = √7056 = 84 cm²
Example 3 — Right Triangle via Heron's: sides 3, 4, 5 → s = 6; Area = √(6×3×2×1) = √36 = 6 = ½×3×4 ✓