Answer:
$15828.75
Step-by-step explanation:
To find the cost of the triangular lot, we first need to find its area.
Given that the dimensions of the triangular lot are 184 feet, 61 feet, and 173 feet.
We can use Heron's formula to find the area of the triangle. Heron's formula states that the area [tex]\sf A [/tex] of a triangle with side lengths [tex]\sf a [/tex], [tex]\sf b [/tex], and [tex]\sf c [/tex] is given by:
[tex]\Large\boxed{\boxed{\sf A = \sqrt{s(s - a)(s - b)(s - c)} }}[/tex]
where
[tex]\sf s = \dfrac{a + b + c}{2} [/tex]
Substituting the given values:
[tex]\sf s = \dfrac{184 + 61 + 173}{2} = \dfrac{418}{2} = 209 [/tex]
Now, we can use Heron's formula to find the area [tex]\sf A [/tex]:
[tex]\sf A = \sqrt{209(209 - 184)(209 - 61)(209 - 173)} [/tex]
[tex]\sf A = \sqrt{209(25)(148)(36)} [/tex]
[tex]\sf A = \sqrt{27838800} [/tex]
[tex]\sf A \approx 5276.2486673772 \, \textsf{ft}^2 [/tex]
Now that we have found the area of the triangular lot, we can find the cost by multiplying the area by the price per square foot:
[tex]\sf \textsf{Cost} = \textsf{Area} \times \textsf{Price per square foot} [/tex]
[tex]\sf \textsf{Cost} = 5276.2486673772 \times \$3 [/tex]
[tex]\sf \textsf{Cost} \approx \$15828.746002131 [/tex]
[tex]\sf \textsf{Cost} \approx \$15828.75 \textsf{(in 2 d.p.)} [/tex]
So, the cost of the triangular lot is approximately $15828.75.
