Figure (A) Shows a Vacant Lot with a 100-Ft Frontage

question 159

Multiple Choice

Figure (a) shows a vacant lot with a 100-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b) . Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor's equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot? ​ ​ ​

• A) 7,900 sq ft
• B) 8,600 sq ft
• C) 8,100 sq ft
• D) 8,400 sq ft

---

Definitions:

Slope

The measure of the steepness or incline of a line on a graph, typically defined as the ratio of the rise over the run between two points.

Vertical Change

The alteration in the y-value or vertical position in a graph, often used in economic models to describe changes in price or quantity.

Seasonally Adjusted

A statistical technique that removes the influences of predictable seasonal patterns to show non-seasonal trends.

Unemployment Rate

The portion of people in the labor market who are without jobs and are searching for employment.