A right-triangular lot has a 120-foot base along its frontage and a perpendicular height of 150 feet. At $12 per square foot, what is the estimated lot value? Assume the rate is market-supported for this subject.
Correct Answer
C) $108,000
Area = 120 ft × 150 ft / 2 = 9,000 SF; indication = 9,000 SF × $12/SF = $108,000. The indicated result is $108,000. Common errors: not halving the base × height for a triangle gives $216,000; converting to square yards before applying the per-square-foot rate gives $12,000; adding the dimensions instead of multiplying them gives $3,240.
Why This Is the Correct Answer
Option C is correct because the triangle's area is 120 feet × 150 feet ÷ 2 = 9,000 square feet. Multiplying by $12 per square foot gives 9,000 × $12 = $108,000.
Why the Other Options Are Wrong
Option A: $3,240
Option A, $3,240, results from adding the dimensions instead of multiplying them: (120 + 150) × $12. The area is 120 × 150 ÷ 2 = 9,000 square feet, so the value is $108,000.
Option B: $12,000
Option B, $12,000, results from converting the 9,000 square feet to 1,000 square yards and then applying the per-square-foot rate. The rate is per square foot, so 9,000 × $12 = $108,000.
Option D: $216,000
Option D, $216,000, results from not halving base × height (120 × 150 × $12). A triangle's area is half of base times height, giving 9,000 square feet and $108,000.
Triangle takes half
A triangle is half of the rectangle formed by its base and height. Multiply base by height, then divide by two.
How to use: Use this whenever a lot or building area is triangular.
Exam Tip
When one choice is exactly double another, check whether a triangle area was left unhalved.
Common Mistakes to Avoid
- -Forgetting to halve base times height
- -Adding dimensions instead of multiplying
- -Converting to square yards with a per-square-foot rate
Concept Deep Dive
Analysis
This question tests finding the area of a right-triangular lot and applying a price per square foot. The area of a triangle is one-half of base times height. Then multiply that area by the supported rate.
Background Knowledge
Irregular lots are often valued by calculating area accurately and applying a market-supported unit rate. Common shapes such as triangles and trapezoids have standard area formulas, and an accurate area is essential before any unit price is applied.
Real-World Application
An appraiser values a corner lot left over from a road realignment that forms a right triangle. The appraiser measures the frontage and depth, calculates the triangular area, and applies a square-foot rate supported by local lot sales.
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