A rectangular lot measures 150 feet by 200 feet. What is the area in acres?
Correct Answer
A) 0.69 acres
150 × 200 = 30,000 square feet. To convert to acres, divide by 43,560 square feet per acre: 30,000 ÷ 43,560 = 0.69 acres.
Why This Is the Correct Answer
Option A is correct because it follows the proper two-step calculation process. First, multiply length × width: 150 feet × 200 feet = 30,000 square feet. Second, convert square feet to acres by dividing by the standard conversion factor: 30,000 ÷ 43,560 = 0.6887, which rounds to 0.69 acres. This demonstrates the correct application of both basic area calculation and the acre conversion formula.
Why the Other Options Are Wrong
Option B: 0.75 acres
Option B (0.75 acres) is incorrect because it represents an error in the conversion calculation, possibly from using an incorrect conversion factor or rounding error. This would equal approximately 32,670 square feet, which doesn't match our calculated area of 30,000 square feet.
Option C: 1.38 acres
Option C (1.38 acres) is incorrect and represents approximately double the correct answer, suggesting a calculation error such as incorrectly squaring one of the dimensions or using the wrong conversion factor. This would equal about 60,000 square feet, which is twice the actual area.
Option D: 30,000 acres
Option D (30,000 acres) is obviously incorrect as it represents the square footage number without any conversion to acres. This is a classic error where the test-taker calculates the square footage correctly but fails to perform the required unit conversion, resulting in an astronomically large area.
The '43,560 Acre Memory Palace'
Remember '43,560' as 'Four Three Five Six Zero' - think of it as '4 quarters, 3 dimes, 5 nickels, 6 pennies, 0 extra' or visualize a football field (about 1.3 acres) and remember that one acre is roughly 3/4 the size of a football field including end zones.
How to use: When you see any area conversion problem, immediately write down '43,560 sq ft = 1 acre' at the top of your scratch work. Calculate square footage first, then divide by 43,560. Always check if your answer makes sense - residential lots are typically 0.1 to 2 acres.
Exam Tip
Always write down the conversion factor (43,560 sq ft = 1 acre) before starting any area problem, and double-check that your final answer is reasonable for the type of property described.
Common Mistakes to Avoid
- -Forgetting to convert square feet to acres and leaving the answer in square feet
- -Using incorrect conversion factors like 40,000 or 45,000 instead of 43,560
- -Making arithmetic errors when multiplying dimensions or dividing by the conversion factor
Concept Deep Dive
Analysis
This question tests the fundamental skill of area calculation and unit conversion that appraisers use daily. It requires calculating the area of a rectangular lot in square feet, then converting to acres using the standard conversion factor. This type of calculation is essential for property valuation, as land area directly impacts property value and is needed for various appraisal methods including the sales comparison approach. Understanding area measurements and conversions is critical since property records, zoning requirements, and market data may be expressed in different units.
Background Knowledge
Appraisers must know that one acre equals exactly 43,560 square feet, which is a standard conversion factor used throughout the real estate industry. Area calculations for rectangular lots use the simple formula: length × width = area in square feet, then divide by 43,560 to convert to acres.
Real-World Application
Appraisers regularly calculate lot sizes when comparing properties in the sales comparison approach, determining if a property meets zoning requirements, or calculating land value per acre. Accurate area calculations are essential for proper property valuation and regulatory compliance.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
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