A 10-acre site has a maximum FAR of 2.0, counting all floor area in this model. Assume four equal floor plates, with no tighter coverage, setback or other limit. What maximum footprint follows from FAR alone?
Correct Answer
C) 217,800 square feet
Site area = 10 × 43,560 = 435,600 square feet. FAR permits 435,600 × 2.0 = 871,200 square feet of counted floor area. Four equal floor plates give 871,200 ÷ 4 = 217,800 square feet of footprint. Unequal floors or tighter applicable controls would change what can be inferred; FAR is not itself lot coverage.
Why This Is the Correct Answer
Option C is correct because the site area is 10 × 43,560 = 435,600 square feet. FAR of 2.0 permits 435,600 × 2.0 = 871,200 square feet of floor area. Spread over four equal floor plates, the footprint is 871,200 ÷ 4 = 217,800 square feet.
Why the Other Options Are Wrong
Option A: 435,600 square feet
Option A, 435,600 square feet, is the site area (10 × 43,560), or equivalently 871,200 ÷ 2 if only two floors were used. The stated four equal floor plates give 871,200 ÷ 4 = 217,800 square feet.
Option B: 108,900 square feet
Option B, 108,900 square feet, results from dividing the site area by four without applying the FAR of 2.0 (435,600 ÷ 4). The correct calculation is 435,600 × 2.0 ÷ 4 = 217,800 square feet.
Option D: 87,120 square feet
Option D, 87,120 square feet, equals 871,200 ÷ 10, as if the total floor area were divided by the 10 acres instead of the four floor plates. The correct calculation is 871,200 ÷ 4 = 217,800 square feet.
Acres, FAR, then floors
Convert acres to square feet, multiply by FAR for total floor area, then divide by the number of equal floors for the footprint.
How to use: Use this sequence whenever a question asks for a footprint from FAR and floor count.
Exam Tip
Do not confuse FAR with lot coverage. Check whether the question imposes any coverage or setback limit that would make the footprint smaller than FAR alone allows.
Common Mistakes to Avoid
- -Forgetting to multiply site area by the FAR
- -Treating FAR as the percentage of land the building may cover
- -Dividing by the wrong number of floors
Concept Deep Dive
Analysis
This question tests converting acres to square feet and using a floor area ratio to find total floor area, then dividing among equal floor plates. FAR limits total floor area relative to site area; it is not lot coverage. With four equal floors and no other limit, the footprint equals total permitted floor area divided by four.
Background Knowledge
Floor area ratio is total counted building floor area divided by site area. An acre equals 43,560 square feet. Lot coverage, setbacks and height limits are separate controls that can further restrict the footprint.
Real-World Application
A developer asks an appraiser about the maximum building on a 10-acre parcel zoned with a 2.0 FAR. The appraiser computes 871,200 square feet of permitted floor area and notes that a four-story building could have a 217,800-square-foot footprint if no other controls apply. The appraiser then checks coverage, setback and parking rules that may reduce it.
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