Triangle Area Calculator

Calculate the area of a triangle using base and height, or Heron's formula when you know all three sides. Get step-by-step solutions with visual diagrams.

Using Base and Height

base (b) height (h)
Formula: A = ½ × base × height

Examples

Example 1: Base and Height

Given: Base = 10 cm, Height = 8 cm

Solution:

A = ½ × 10 × 8 = 40 cm²

Example 2: Heron's Formula

Given: Sides = 3, 4, 5 units

Solution:

s = (3+4+5)/2 = 6

A = √(6×3×2×1) = √36 = 6 sq units

Example 3: Equilateral Triangle

Given: Side = 6 cm

Solution:

s = 9, A = √(9×3×3×3) = 9√3 ≈ 15.59 cm²

Example 4: Isosceles Triangle

Given: Base = 8 m, Height = 6 m

Solution:

A = ½ × 8 × 6 = 24 m²

Example 5: Right Triangle

Given: Legs = 5 ft, 12 ft

Solution:

Using legs as base and height:

A = ½ × 5 × 12 = 30 ft²

About Triangle Area Calculations

Methods for Calculating Triangle Area

There are several ways to calculate the area of a triangle, depending on what information you have:

1. Base and Height Method

This is the most common method when you know the base and the perpendicular height from that base to the opposite vertex.

A = ½ × base × height

2. Heron's Formula

Use this method when you know all three sides but not the height. First, calculate the semi-perimeter:

s = (a + b + c) / 2
A = √(s(s-a)(s-b)(s-c))

3. Special Cases

  • Equilateral Triangle: A = (√3/4) × side²
  • Right Triangle: The two legs serve as base and height
  • Using Trigonometry: A = ½ × a × b × sin(C)

Triangle Inequality

For a triangle to exist with three given sides, the sum of any two sides must be greater than the third side:

  • a + b > c
  • b + c > a
  • a + c > b