Heron's formula

Heron's formula allows you to find the area of any triangle if you know the lengths of all three sides. You do not need to know the height or any angles. First, calculate the semi-perimeter $s$ of the triangle: $s = \frac{a + b + c}{2}$ where $a$, $b$, and $c$ are the side lengths. Then, the area $A$ is given by: $A = \sqrt{s(s-a)(s-b)(s-c)}$

Important properties

• Works for any triangle (not just right or equilateral triangles).

• Requires only the side lengths.

• The formula uses the semi-perimeter, which is half the sum of the side lengths.

• If any side is longer than the sum of the other two, the area becomes zero (triangle inequality).