The survey plat in the figure shows two lots that form a trapezold. The measures of the parallel sides are $116.60 \mathrm{f}$ and $174.00 \mathrm{f}$. The height of the trapezoid is $165.38 \mathrm{f}$. Find the combined area of the two lots:
Calculating the above expression, we find that the combined area of the two lots is \( \boxed{24029.714} \) square feet.
Step 1 :The problem provides the measures of the parallel sides of a trapezoid as $116.60 \mathrm{f}$ and $174.00 \mathrm{f}$, and the height of the trapezoid as $165.38 \mathrm{f}$. We are asked to find the combined area of the two lots that form this trapezoid.
Step 2 :We know that the area of a trapezoid is given by the formula: \( \text{Area} = \frac{1}{2} \times (\text{sum of the lengths of the parallel sides}) \times \text{height} \)
Step 3 :Substituting the given values into the formula, we get: \( \text{Area} = \frac{1}{2} \times (116.6 + 174.0) \times 165.38 \)
Step 4 :Calculating the above expression, we find that the combined area of the two lots is \( \boxed{24029.714} \) square feet.