A lot is 100 feet wide and 150 feet deep. Setbacks are 25 feet front, 20 feet rear and 10 feet on each side. What is the buildable footprint?
Correct Answer
C) 8,400 square feet
Why this is correct: The buildable footprint is the area within setbacks. Width: 100 ft - (10 ft left + 10 ft right) = 80 ft. Depth: 150 ft - (25 ft front + 20 ft rear) = 105 ft. Area: 80 ft × 105 ft = 8,400 sq ft. Why the other choices are wrong: "15,000 square feet" is the raw lot area (100×150), ignoring setbacks. "10,500 square feet" might incorrectly subtract only front/rear or side setbacks. "12,000 square feet" is not supported by the calculation. Exam tip: Always subtract setbacks from total dimensions before calculating buildable area; this is a common exam math step.
Why This Is the Correct Answer
Subtracting both side setbacks from the width gives 80 feet, subtracting front and rear from the depth gives 105 feet, and the product is 8,400 square feet. Pairing each setback with the dimension it actually reduces is the discipline the item tests. The result is a footprint, meaning the ground-floor area available, not the total buildable floor area, which would depend on permitted stories. Checking the result against the raw lot area confirms it should be meaningfully smaller.
Why the Other Options Are Wrong
Option A: 15,000 square feet
15,000 square feet is the raw lot area of 100 by 150, computed as though no setbacks existed. It answers what the parcel measures rather than what can be built on. Any answer equal to the full lot area in a setback problem has skipped the entire calculation.
Option B: 10,500 square feet
10,500 square feet results from subtracting only the front and rear setbacks, giving 100 by 105, and forgetting the two side setbacks entirely. It is the most instructive wrong answer because it shows a partial application of the right method. Working both dimensions before multiplying prevents it.
Option D: 12,000 square feet
12,000 square feet does not follow from any consistent subtraction of the stated setbacks and may come from subtracting one setback from each dimension rather than two. Setbacks apply on all four sides, so each dimension loses two of them. Sketching the lot with all four setbacks drawn in makes the error visible.
Two Bites From Each Dimension
Every dimension loses two setbacks, one from each end. Sides come off the width; front and rear come off the depth. Sketch the rectangle inside the rectangle before you multiply.
How to use: Draw the lot, mark all four setbacks, then compute the inner rectangle's dimensions separately before multiplying. Confirm your answer is meaningfully smaller than the raw lot area.
Exam Tip
Footprint is not buildable floor area. If a question supplies a height limit or a floor area ratio, an additional step is required after the envelope is computed.
Common Mistakes to Avoid
- -Subtracting only one setback from each dimension
- -Reporting raw lot area as the buildable area
- -Treating the footprint as total buildable floor area without applying height or floor area ratio limits
Concept Deep Dive
Analysis
Setbacks are minimum distances a structure must stand back from each lot line, imposed by zoning to control light, air, fire separation, and streetscape. The buildable envelope, sometimes called the building footprint or building envelope, is what remains after subtracting them, and computing it correctly requires treating each pair of opposing lines separately. Width runs between the two side lines, so both side setbacks come off the 100-foot width: 100 minus 10 minus 10 leaves 80 feet. Depth runs between front and rear, so those two come off the 150-foot depth: 150 minus 25 minus 20 leaves 105 feet. Multiplying gives 8,400 square feet, or 56 percent of the 15,000-square-foot lot. That fraction matters to a developer, because a lot's raw area is not what can be built on, and setbacks bind hardest on small or narrow lots. The buildable envelope is also only the horizontal constraint; height limits, floor area ratio, parking requirements, and lot coverage maximums can each reduce the usable building program further.
Background Knowledge
You need the zoning vocabulary of setbacks, buildable envelope, lot coverage, floor area ratio, and height limits, and how each constrains development. You should also know the highest and best use tests of legally permissible and physically possible, and that a footprint differs from total buildable floor area.
Real-World Application
An appraiser testing highest and best use on an infill lot computes the buildable envelope from the setbacks, checks it against the maximum lot coverage percentage and the required parking, finds parking rather than setbacks is the binding constraint, and documents that finding in her analysis.
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