Basic Derivation of Heron’s Formula
Introduction This post is a basic derivation of the famous Heron’s formula, which allows calculation of the area of any triangle in terms of its side lengths . We refer to the following diagram: As is convention, let sides be opposite to angles . Further, let the altitude length and . Then, by the Pythagorean Theorem applied to triangles and , we have the following two equations: Subtracting the two equations cancels the and yields ….