01 · FORMULA & DEFINITION
Heron's Formula Statement
For a triangle with side lengths a, b, and c:
1. Semi-perimeter (s): s = (a + b + c) / 2
2. Area of Triangle: Area = √[ s (s - a) (s - b) (s - c) ]
SOLVED EXAMPLE
Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm
1. Calculate semi-perimeter s:
s = (13 + 14 + 15) / 2 = 42 / 2 = 21 cm
2. Apply Heron's Formula:
Area = √[ 21 × (21 - 13) × (21 - 14) × (21 - 15) ]
= √[ 21 × 8 × 7 × 6 ]
= √[ (7 × 3) × (4 × 2) × 7 × (3 × 2) ]
= √[ 7² × 3² × 4² ] = 7 × 3 × 4 = 84 cm²
= √[ 21 × 8 × 7 × 6 ]
= √[ (7 × 3) × (4 × 2) × 7 × (3 × 2) ]
= √[ 7² × 3² × 4² ] = 7 × 3 × 4 = 84 cm²