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.
Given: Base = 10 cm, Height = 8 cm
Solution:
A = ½ × 10 × 8 = 40 cm²
Given: Sides = 3, 4, 5 units
Solution:
s = (3+4+5)/2 = 6
A = √(6×3×2×1) = √36 = 6 sq units
Given: Side = 6 cm
Solution:
s = 9, A = √(9×3×3×3) = 9√3 ≈ 15.59 cm²
Given: Base = 8 m, Height = 6 m
Solution:
A = ½ × 8 × 6 = 24 m²
Given: Legs = 5 ft, 12 ft
Solution:
Using legs as base and height:
A = ½ × 5 × 12 = 30 ft²
There are several ways to calculate the area of a triangle, depending on what information you have:
This is the most common method when you know the base and the perpendicular height from that base to the opposite vertex.
Use this method when you know all three sides but not the height. First, calculate the semi-perimeter:
For a triangle to exist with three given sides, the sum of any two sides must be greater than the third side: