Heron's Formula

A=s(sa)(sb)(sc)A = \sqrt{s(s-a)(s-b)(s-c)}

Description

Calculates triangle area using only side lengths.

Variables

Symbol Meaning
A Area
a, b, c Side lengths
s Semi-perimeter = (a+b+c)/2

Example

Problem

Find area with sides 3, 4, 5

Solution

s = 6, A = √(6·3·2·1) = 6

Real-World Applications

  • Surveying
  • Construction
  • Navigation