Chapter 8.4, Problem 49AYU

Bretschneider’s Formula There is a Heron-type formula that can be used to find the area of a general quadrilateral.

$K=\sqrt{\left(s-a\right)\left(s-b\right)\left(s-c\right)\left(s-d\right)-abcd{\cos }^2\theta }$

Where $a,b,c$ and $d$ are the side lengths, $\theta$ is half the sum of two opposite angles, and $s$ is half the perimeter.

Show that if a triangle is considered a quadrilateral with one side equal to $0$, Bretschneider’s Formula reduces to Heron’s Formula.