A parcel of land is 400 feet by 640 feet. The parcel is cut in half diagonally by a stream. How many acres are in each half of the parcel?
A) 2.75
B) 2.94
C) 5.51
D) 5.88
Answer (2)
Calculate the total area of the rectangular parcel: A re a = 400 ft × 640 ft = 256000 ft 2 .
Determine the area of each half: A re a ha l f = 2 256000 ft 2 = 128000 ft 2 .
Convert the area from square feet to acres: A re a a cres = 43560 ft 2 / acre 128000 ft 2 ≈ 2.938 acres .
Round to two decimal places: Each half is approximately 2.94 acres.
Explanation
Problem Analysis We are given a rectangular parcel of land that is 400 feet by 640 feet. The parcel is cut in half diagonally by a stream, and we need to find the area of each half in acres.
Calculations First, we calculate the total area of the rectangular parcel in square feet: A re a = l e n g t h × w i d t h = 400 feet × 640 feet = 256000 square feet Since the parcel is cut in half diagonally, each half has an area of: A re a ha l f = 2 A re a = 2 256000 square feet = 128000 square feet Now, we convert the area of each half from square feet to acres, using the conversion factor 1 acre = 43,560 square feet: A re a a cres = 43560 A re a ha l f = 43560 square feet/acre 128000 square feet ≈ 2.938475665748393 acres Rounding the result to two decimal places, we get 2.94 acres.
Final Answer Therefore, each half of the parcel contains approximately 2.94 acres.
Examples
Understanding how to calculate land area is crucial in real estate, agriculture, and urban planning. For instance, when dividing a plot of land for different uses like farming and building, knowing the exact acreage helps in fair distribution and efficient resource allocation. Imagine you're a farmer wanting to split a field to grow different crops; accurate area calculations ensure each crop gets the necessary space for optimal yield. Similarly, developers use these calculations to plan housing layouts and green spaces effectively.
The area of each half of a 400 ft by 640 ft parcel of land is approximately 2.94 acres after calculating the total area, dividing by two, and converting to acres. The chosen option is B) 2.94.
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