Question

You are considering purchasing the piece of property above. It is bordered

on the north by the Holy Wah River, on the south by Piikkisika Avenue, on the east by
Heikki Lunta Drive, and on the west by Thirty Pointer Highway. The piece of property is
advertised to be 1.40 acres. You are curious if that number is accurate.
You have access to the property for a weekend and do some measuring. You come up
with the coordinates of the points shown above, using Piikkisika Avenue as the x-axis
and Thirty Pointer Highway as the y-axis. All coordinates have measurements in yards.
B(25, 70) C(50, 60) D(75, 55)
A(0, 75)
Using these coordinates, use a Riemann Sum along with the ideas developed in class to
decide if the property is being advertised correctly as 1.40 acres. Show your calculations
as well as your conclusion below. Do you think that the property is being properly
advertised as 1.40 acres?
Hint: 1 acre = 4840 yd²

Answer 1

By dividing the property into four rectangles and calculating the area of each rectangle, we can determine that the actual area of the property is approximately 0.2841 acres.

Step-by-step explanation:

To determine if the property is being advertised correctly as 1.40 acres, we can use a Riemann Sum. A Riemann Sum is used to approximate the area under a curve by dividing it into small rectangles.

In this case, we can divide the property into four rectangles using the given coordinates. The height of each rectangle will be the difference in y-coordinates, and the width will be the difference in x-coordinates.

We can then calculate the area of each rectangle and add them up to get the total area of the property.

Let's calculate:

Rectangle 1: Length = 25 - 0 = 25 yards,

Width = 70 - 0 = 70 yards

Rectangle 2: Length = 50 - 25 = 25 yards,

Width = 60 - 55 = 5 yards

Rectangle 3: Length = 75 - 50 = 25 yards,

Width = 55 - 60 = -5 yards (negative because the rectangle is below the x-axis)

Rectangle 4: Length = 0 - 75 = -75 yards (negative because the rectangle is to the left of the y-axis),

Width = 75 - 70 = 5 yards

Adding up the areas of each rectangle:

Area = (25 yards * 70 yards) + (25 yards * 5 yards) + (25 yards * -5 yards) + (-75 yards * 5 yards)

Area = 1750 square yards + 125 square yards - 125 square yards - 375 square yards

Area = 1375 square yards

Finally, let's convert this area to acres:

Area = 1375 square yards * (1 acre / 4840 square yards)

Area = 0.2841 acres

Based on our calculations, the property is not being properly advertised as 1.40 acres. The actual area of the property is approximately 0.2841 acres.