In my previous blog titled “An Algebraic Proof of Heron’s Formula“, I algebraically derived the Heron’s formula concerning A, the area of a triangle:
where a, b, c are three sides of a triangle and .
There is an alternative derivation which requires some basic trigonometry.
Here it is:
Let (see Fig. 1), then
due to trigonometric identity .
Moreover, by the law of cosines, which implies
and (1) becomes