Answer
The land would cost about $165,554
Work Step by Step
First, one must find the area using Heron's formula: $\sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is half of the perimeter of the triangle:
$s=\frac{1}{2}(a+b+c)$
$s=\frac{1}{2}(112+148+190)=\frac{1}{2}(450)=225$
Now, we can find the area:
$A=\sqrt{225(225-112)(225-148)(225-190)}$
$A=\sqrt{225(113)(77)(35)}$
$A=\sqrt{68,520,375}\approx8278$ ft$^2$
Since the land is valued at \$20 per ft$^2$, using $\frac{\$20}{1ft^2}=\frac{?}{8278 ft^2}$ will determine the land's value:
$8278\cdot \$20= \$165,554$
