An irregular-shaped lot has the following dimensions: Side A = 100', Side B = 150', Side C = 80', Side D = 120'. Using the coordinate method, the surveyor calculated the area as 11,500 square feet. How many acres is this?
Correct Answer
B) 0.26 acres
Why this is correct: 1 acre = 43,560 square feet. To convert square feet to acres, divide the area in square feet by 43,560. Calculation: 11,500 sq ft / 43,560 sq ft per acre = approximately 0.264 acres, which rounds to 0.26 acres. Why the other choices are wrong: 0.46 acres results from dividing by an incorrect number (e.g., 25,000). 11.5 acres mistakenly treats square feet as acres. 2.64 acres results from dividing by 4,356 instead of 43,560. Exam tip: Memorize the conversion: 43,560 sq ft = 1 acre. For small lots, the acreage will be a decimal less than 1.
Why This Is the Correct Answer
Option A is correct because it properly applies the square feet to acres conversion formula. The calculation is 11,500 ÷ 43,560 = 0.264 acres, which rounds to 0.26 acres. This demonstrates the standard conversion where 43,560 square feet equals exactly one acre. The answer shows proper rounding to two decimal places, which is typical in real estate practice.
Why the Other Options Are Wrong
Option A: 0.46 acres
Option A (0.46 acres) appears to result from an incorrect conversion factor or calculation error, possibly using an approximation like 25,000 square feet per acre instead of the correct 43,560.
Option C: 11.5 acres
Option C (11.5 acres) incorrectly assumes that the square footage number directly equals the acreage, ignoring the conversion factor entirely. This represents a fundamental misunderstanding of area measurement units.
Option D: 2.64 acres
Option D (2.64 acres) represents a decimal place error, likely from dividing by 4,356 instead of 43,560, or multiplying by 0.264 by 10. This would result in an area that's 10 times too large.
The 43,560 Memory Palace
Remember '43,560' as 'For (4) Three (3) Five-Star (5) Six (6) Officers (0)' - imagine 4 groups of 3 five-star military officers, with 6 in each group, plus 0 extras, all standing on one acre of land.
How to use: When you see any square footage conversion question, immediately recall the military officers on their acre of land and write down 43,560 as your conversion factor before doing any calculations.
Exam Tip
Always write down '1 acre = 43,560 sq ft' at the top of your scratch paper when the exam begins, as this conversion appears frequently and calculation errors are common under time pressure.
Common Mistakes to Avoid
- -Using 40,000 or 45,000 as approximations instead of the exact 43,560
- -Decimal place errors when dividing, especially forgetting to move the decimal point
- -Confusing the conversion direction and multiplying instead of dividing
Concept Deep Dive
Analysis
This question tests the fundamental skill of converting square feet to acres, which is essential in real estate appraisal. The question provides an irregular lot with given dimensions and a calculated area in square feet, requiring conversion to acres using the standard conversion factor. While the individual side dimensions are provided, they serve as a distractor since the total area has already been calculated by the surveyor using the coordinate method. The key is recognizing that regardless of the lot's shape or how the area was calculated, the conversion from square feet to acres always uses the same factor of 43,560 square feet per acre.
Background Knowledge
One acre equals exactly 43,560 square feet, which derives from the historical definition of an acre as a furlong (660 feet) times a chain (66 feet). This conversion factor is fundamental to real estate and must be memorized for appraisal work.
Real-World Application
Appraisers constantly convert between square feet and acres when analyzing comparable sales, as MLS listings might show lot sizes in square feet while appraisal reports typically express larger lots in acres for easier comprehension by clients and lenders.
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