A rectangular parcel of land that measures one-half mile on one side and one-quarter mile on the other side would contain how many acres of land? Select one: a. 640 b. 320 c. 160 d. 80
The correct answer and explanation is:
The correct answer is d. 80 acres.
To calculate the area of the land in acres, we first need to find the area in square miles and then convert it into acres.
- Find the area of the land in square miles:
The dimensions of the land are given as 1/2 mile on one side and 1/4 mile on the other side. To calculate the area in square miles, multiply the two dimensions: Area=12 mile×14 mile=18 square miles\text{Area} = \frac{1}{2} \, \text{mile} \times \frac{1}{4} \, \text{mile} = \frac{1}{8} \, \text{square miles} - Convert square miles to acres:
1 square mile is equal to 640 acres. To convert from square miles to acres, multiply the area in square miles by 640: Area in acres=18 square miles×640 acres/square mile=80 acres\text{Area in acres} = \frac{1}{8} \, \text{square miles} \times 640 \, \text{acres/square mile} = 80 \, \text{acres}
Thus, the rectangular parcel of land has an area of 80 acres.
This calculation follows the principle that the area in square miles is first determined by multiplying the length and width of the land. Then, this result is converted into acres using the standard conversion factor (1 square mile = 640 acres). The result is a simple multiplication to determine the total acreage of the land parcel.