Answer
No, see explanations.
Work Step by Step
Step 1. Given a total budget of $10,000$ dollars, with a cost of $2+0.1=2.1$ dollars per square feet, we need to calculate the total area and then the total cost.
Step 2. The area can be approximated as the sum of individual sections. Each section can be approximated using a trapezoid (middle point approximation) with a height of $15\ ft$ and the top and bottom width given in the figure of the exercise.
Step 3. We have the total area as
$A=\frac{15}{2}(0+2(36+54+51+49.5+54+64.4+67.5)+42)=5961\ ft^2$
Step 4. The total cost will be
$T=5961\times 2.1=12,518.1\gt 10,000$
which means that the cost is more than the budget. We conclude that the lot can not be built for $10,000$ dollars.
