A three-acre site is zoned with a maximum floor area ratio of 0.5. How much building area does that permit?
Correct Answer
A) 65,340 square feet
Why this is correct: First, convert acres to square feet: 3 acres * 43,560 square feet per acre = 130,680 square feet. A Floor Area Ratio (FAR) of 0.5 means the building area can be 0.5 times the site area. Calculate: 130,680 * 0.5 = 65,340 square feet of permitted building area. Why the other choices are wrong: 43,560 square feet is the area of one acre, not the answer. 130,680 square feet is the total site area, not the building area. 21,780 square feet is one-quarter of the site area, not half. Exam tip: FAR = (Building Area) / (Site Area). So, Building Area = FAR * Site Area. Always confirm units (acres to sq ft).
Why This Is the Correct Answer
Option A is correct at 65,340 square feet. Converting three acres gives 130,680 square feet of site area, and applying the 0.5 ratio gives 65,340 square feet of permitted floor area. The ratio multiplies the site area rather than dividing it, which is the step the distractors probe. Actual buildable area may be less once setbacks, height limits, parking, and open space requirements are applied, so the ratio establishes a ceiling rather than a guarantee.
Why the Other Options Are Wrong
Option B: 43,560 square feet
43,560 square feet is simply the number of square feet in one acre, carried into the answer without any calculation. It ignores both the three-acre site size and the floor area ratio. Recognizing the figure as a conversion constant rather than a result is enough to eliminate it.
Option C: 130,680 square feet
130,680 square feet is the total site area before the ratio is applied, so this choice stops one step short. A ratio of 0.5 means the building may cover the equivalent of half the site area, not all of it, and selecting the site area would imply a ratio of 1.0. Reading the ratio as a limit that must still be applied avoids this error.
Option D: 21,780 square feet
21,780 square feet is half of one acre, produced by applying the ratio to a single acre instead of to the full three-acre site. The error is dropping the site size partway through the calculation. Converting the entire site first, then applying the ratio once, keeps the steps in order.
Ratio times site
Floor area ratio is a multiplier on the ground you own. Convert acres to square feet first, then multiply. A ratio under one always yields less building than site.
How to use: Write the conversion and the multiplication as two separate lines. Then check the direction: a ratio below one must produce an answer smaller than the site area.
Exam Tip
Treat the floor area ratio as a ceiling. Setbacks, height limits, and parking frequently prevent a project from reaching it, which matters for feasibility even though the arithmetic is simple.
Common Mistakes to Avoid
- -Forgetting to convert acres to square feet
- -Dividing by the ratio instead of multiplying
- -Treating the ratio as a footprint limit rather than a total floor area limit
- -Assuming the full permitted area is achievable without checking setbacks and parking
Concept Deep Dive
Analysis
This tests floor area ratio, the zoning device that caps development intensity by tying permitted building area to site area. Floor area ratio is gross building floor area divided by site area, so permitted building area equals the ratio multiplied by the site. The calculation requires a unit conversion first, since zoning expresses site area in square feet while land is often described in acres: three acres at 43,560 square feet per acre is 130,680 square feet, and half of that is 65,340 square feet of permitted building area. Note that the ratio governs total floor area across all stories rather than footprint, so a 0.5 ratio might be achieved as a single-story building covering half the lot or a two-story building covering a quarter of it, subject to setbacks, height limits, and parking requirements. Appraisers rely on this measure when valuing land on a price-per-buildable-square-foot basis, which is often the most meaningful unit of comparison for development sites.
Background Knowledge
You need the definition of floor area ratio as gross building area divided by site area, and the conversion of 43,560 square feet per acre. You should also know that the ratio caps total floor area across all stories rather than footprint, that setbacks, height limits, parking, and open space can bind before the ratio does, and that development sites are often analyzed on a price-per-buildable-square-foot basis.
Real-World Application
Valuing an infill development parcel, you compute the permitted floor area under the zoning, confirm parking requirements do not bind before the ratio does, and analyze comparable land sales on a price-per-buildable-square-foot basis so parcels of differing size and intensity become comparable.
More Land/Site Questions
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