A 10-acre site is zoned for office development with a maximum floor area ratio (FAR) of 2.0. If the developer plans a 4-story building, what is the maximum building footprint?
Correct Answer
C) 217,800 square feet
With 10 acres (435,600 sq ft) and FAR of 2.0, maximum building area is 871,200 sq ft. For a 4-story building, the maximum footprint is 871,200 ÷ 4 = 217,800 sq ft.
Why This Is the Correct Answer
Option C correctly applies the FAR calculation methodology. First, convert 10 acres to square feet (10 × 43,560 = 435,600 sq ft). Then multiply by the FAR of 2.0 to get maximum total building area (435,600 × 2.0 = 871,200 sq ft). Finally, divide by the number of stories to find maximum footprint (871,200 ÷ 4 = 217,800 sq ft). This represents the largest ground floor area possible while staying within zoning constraints.
Why the Other Options Are Wrong
Option A: 87,120 square feet
This answer appears to be the result of dividing the total allowable building area by 10 instead of 4, or possibly confusing the calculation steps and using an incorrect conversion factor.
Option B: 108,900 square feet
This answer likely results from an error in the acre-to-square-feet conversion or incorrectly applying the FAR multiplier, possibly using 2.5 instead of 2.0 as the FAR.
Option D: 435,600 square feet
This answer represents the total lot size in square feet (10 acres = 435,600 sq ft) without any FAR calculation, indicating a fundamental misunderstanding of what the question is asking for.
FAR-STORY Method
FAR × Acres × 43,560 ÷ Stories = Footprint. Remember the acronym FAAS: FAR, Acres (converted), All stories, Solution (divide total by stories).
How to use: When you see FAR problems, immediately write down FAAS and fill in each component: identify the FAR, convert acres to square feet, calculate total allowable area, then divide by stories for footprint.
Exam Tip
Always convert acres to square feet first (multiply by 43,560), then apply FAR, then divide by stories - work systematically through each step to avoid calculation errors.
Common Mistakes to Avoid
- -Forgetting to convert acres to square feet
- -Confusing FAR with lot coverage ratio
- -Using the wrong conversion factor for acres (using 40,000 instead of 43,560)
Concept Deep Dive
Analysis
This question tests understanding of Floor Area Ratio (FAR) calculations and their relationship to building footprint in zoning analysis. FAR is a critical zoning control that limits the total building area relative to the lot size, regardless of how that area is distributed vertically. The concept requires understanding the mathematical relationship between total allowable building area, number of stories, and the resulting maximum footprint. This type of calculation is fundamental in highest and best use analysis and development feasibility studies.
Background Knowledge
Floor Area Ratio (FAR) is calculated as the total building floor area divided by the lot area, and is used by municipalities to control building density. One acre equals 43,560 square feet, a conversion that appraisers must memorize for exam calculations.
Real-World Application
Appraisers use FAR calculations when analyzing highest and best use for development sites, determining if proposed developments comply with zoning, and estimating development potential for valuation purposes.
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