Chapter 8.4, Problem 46AE

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

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

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

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

(b) Use Bretschneiders’s Formula to find the area of the lot for side in Problem 39, rounded to the nearest square foot. Do the results agree?