A lot measures 120 feet by 180 feet. Comparable sites sell at $6.00 per square foot. What value is indicated? Assume the comparable unit rate is supported for this subject without further adjustment.
Correct Answer
D) $129,600
Area = 120 ft × 180 ft = 21,600 SF; value = 21,600 SF × $6/SF = $129,600. The indicated value is $129,600. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: converting to square yards before applying the per-square-foot rate gives $14,400; using the perimeter instead of the area gives $3,600; treating the rectangle as a triangle gives $64,800.
Why This Is the Correct Answer
Option D is correct because 120 feet × 180 feet = 21,600 square feet, and 21,600 × $6.00 = $129,600. The rate is per square foot, matching the area units. Applying it to the full area gives the indicated value.
Why the Other Options Are Wrong
Option A: $3,600
Option A, $3,600, uses the perimeter instead of the area: (120 + 180) × 2 = 600 feet, and 600 × $6 = $3,600. The rate applies to square feet of area: 21,600 × $6 = $129,600.
Option B: $14,400
Option B, $14,400, converts the area to square yards before applying a per-square-foot rate: 21,600 ÷ 9 × $6 = $14,400. The rate is per square foot, so the correct value is 21,600 × $6 = $129,600.
Option C: $64,800
Option C, $64,800, treats the rectangle as a triangle by halving the area: 120 × 180 × $6 ÷ 2 = $64,800. A rectangle's area is width × depth with no halving, giving $129,600.
Rectangle: width times depth
A rectangle's area is width times depth with no halving; only triangles take half.
How to use: Use this when a lot's dimensions are given and you need its square footage.
Exam Tip
Write down the area before multiplying by the rate so you can spot perimeter or halving errors.
Common Mistakes to Avoid
- -Using the perimeter in place of the area
- -Dividing by 9 when the rate is already per square foot
Concept Deep Dive
Analysis
This question tests calculating the area of a rectangular lot and applying a per-square-foot rate. Width times depth gives the square footage, and that is multiplied by the supported rate. The question confirms no further adjustment is needed.
Background Knowledge
The area of a rectangle is width multiplied by depth, while a triangle's area is half the base times the height. Price per square foot is one of the standard units of comparison for vacant land. Units of the rate and the area must match.
Real-World Application
A residential lot measures 120 by 180 feet. Comparable lot sales support $6 per square foot, so the appraiser computes 21,600 square feet and an indicated land value of $129,600.
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