## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Review Exercises - Page 798: 21

$\$214,194$. #### Work Step by Step Heron’s formula to find the area of the triangle is given by:$\text{Area}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$Where$s=\frac{a+b+c}{2}$Here,$a=260,b=320,c=450$So,$\begin{align} & s=\frac{260+320+450}{2} \\ & =\frac{1030}{2} \\ & =515 \end{align}$So, the area of the triangle is$\begin{align} & \sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}=\sqrt{515\left( 515-260 \right)\left( 515-320 \right)\left( 515-450 \right)} \\ & =\sqrt{515\times 255\times 195\times 65} \\ & =\sqrt{1664,544,375} \\ & \approx 40,798.83 \end{align}$So, the area of the triangle is approximately$40,798.83$square feet. Now, the cost of the triangular lot will be$40,798.83\times 5.25\approx 214,194$. So, the cost to the nearest dollar of the triangular lot is$\$214,194$.

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