Question

Cost of a Triangular Lot The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is $3 per square foot, how much does the lot cost?

Short answer

The cost of lot is $5446.38.

Step-by-step solution

Step 1. Given information.

Dimensions of a triangular lot are 100 feet by 50 feet by 75 feet.

Cost of land is $3 per square foot.

Step 2. Determine the semi perimeter of the triangular lot.

The semi perimeter of the triangular lot is:

$\begin{array}{rcl}s& =& \frac{a+b+c}{2}\\ & =& \frac{100+50+75}{2}\\ & =& \frac{225}{2}\\ & =& 112.5\end{array}$

Step 3. Determine the area of the triangle.

Area of the triangular lot is:

$\begin{array}{rcl}A& =& \sqrt{s(s-a)(s-b)(s-c)}\\ & =& \sqrt{112.5(112.5-100)(112.5-50)(112.5-75)}\\ & =& \sqrt{112.5(12.5)(62.5)(37.5)}\\ & =& \sqrt{3295898.4375}\\ & \approx & 1815.46\end{array}$

Step 4. Determine the cost of lot.

Cost of land is $3 per square foot. So, the total cost is:

$\begin{array}{rcl}Cost& =& \$3\times 1815.46\\ & =& \$5446.38\end{array}$

The cost of lot is $5446.38.