Heron's Formula: Finding the Area of Any Triangle
🎯 Big Idea
What if you know all three sides of a triangle but not the height? Heron's Formula lets you calculate the area using only the three side lengths — no altitude needed!
📜 A Bit of History
This formula is named after Heron of Alexandria, a Greek mathematician and engineer who lived around 60 AD. He published this formula in his work Metrica, though some historians believe it was known even earlier by Archimedes.
📐 The Formula
Given a triangle with sides of length $a$, $b$, and $c$:
Step 1: Calculate the Semi-Perimeter
The semi-perimeter is half the perimeter of the triangle:
$$ s = \frac{a + b + c}{2} $$
Step 2: Apply Heron's Formula
$$ A = \sqrt{s(s-a)(s-b)(s-c)} $$
where:
- $A$ = area of the triangle
- $s$ = semi-perimeter
- $a, b, c$ = lengths of the three sides