Heron's Formula/Proof 2

Proof
A triangle can be considered as a cyclic quadrilateral one of whose sides has degenerated to zero.

From Brahmagupta's Formula, the perimeter of a cyclic quadrilateral is given by:
 * $\sqrt {\paren {s - a} \paren {s - b} \paren {s - c} \paren {s - d}}$

where $s$ is the semiperimeter:
 * $s = \dfrac {a + b + c + d} 2$

The result follows by letting $d$ tend to zero.