Answer
$\$214,194$.
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 $\$214,194$.
