Class 9 · Chapter 10

Heron's Formula

Formula to compute the area of a triangle when all three sides are known.

Watch this chapter

Read the full chapter

Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

The standard formula

\text{area} = \tfrac{1}{2}\cdot \text{base}\cdot \text{height}

requires knowing the altitude. Heron's formula lets you compute area from just the three side-lengths, no altitude required.

Key concepts & formulas

Semi-perimeter

s = (a+b+c)/2

Area

= \sqrt{s(s-a)(s-b)(s-c)}

Works for any triangle (right, isosceles, scalene).

For a right triangle it matches

\tfrac{1}{2}\cdot

base

\cdot

height.

For equilateral of side

a

: area

= \tfrac{\sqrt 3}{4}a^2

Useful when altitude/height is unknown.