A triangular lot has frontage of 120 feet and a depth of 150 feet. Using a price of $12 per square foot, what is the estimated lot value?
Correct Answer
B) $108,000
Why this is correct: For a right triangle, area = (base * height) / 2. Here, base = 120 ft, depth = 150 ft. Area = (120 * 150) / 2 = 18000 / 2 = 9000 sq ft. Value = Area * Price per sq ft = 9000 * 12 = 108000. Why the other choices are wrong: 144000 incorrectly uses a rectangular area (120*150). 180000 is the area before dividing by 2. 216000 is double the rectangular area value. Exam tip: For triangular lots, remember the area formula is half of a rectangle. Always divide by 2.
Why This Is the Correct Answer
Option A is correct because it properly applies the triangular area formula: Area = (base × height) ÷ 2. With a frontage (base) of 120 feet and depth (height) of 150 feet, the calculation is (120 × 150) ÷ 2 = 18,000 ÷ 2 = 9,000 square feet. Multiplying this area by the given price of $12 per square foot yields 9,000 × $12 = $108,000. This demonstrates the correct sequence of geometric calculation followed by unit pricing application.
Why the Other Options Are Wrong
Option A: $144,000
$144,000 represents a calculation error where someone likely forgot to divide by 2 in the triangular area formula, treating it like a rectangle: 120 × 150 = 18,000 sq ft, then incorrectly calculating 18,000 × $12 ÷ 1.5 = $144,000, or making some other computational mistake.
Option C: $180,000
$180,000 would result from calculating the area as a rectangle (120 × 150 = 18,000 sq ft) and then multiplying by $10 per square foot instead of $12, or from some other combination of errors in both area calculation and unit pricing.
Option D: $216,000
$216,000 represents the most common error: calculating the area as if it were a rectangle rather than a triangle, yielding 120 × 150 = 18,000 square feet, then multiplying by $12 per square foot (18,000 × $12 = $216,000) without applying the ÷2 factor for triangular area.
Triangle Half-Time Rule
Remember 'Triangles Take Half-Time' - when you see a triangle, always think 'half of rectangle.' The formula becomes: Triangle = Rectangle ÷ 2, or (base × height) ÷ 2. Visualize cutting a rectangle diagonally in half.
How to use: When you see 'triangular lot' in a question, immediately think 'Half-Time!' and remember to divide your base × height calculation by 2 before applying any unit pricing. This prevents the most common error of treating triangular lots like rectangular ones.
Exam Tip
Always write down the area formula first before plugging in numbers. For triangles, write 'Area = (b × h) ÷ 2' at the top of your calculation to avoid forgetting the division by 2 step.
Common Mistakes to Avoid
- -Forgetting to divide by 2 and treating the triangle as a rectangle
- -Confusing which measurement is the base versus the height
- -Applying the wrong unit price or making arithmetic errors in the final multiplication
Concept Deep Dive
Analysis
This question tests the fundamental skill of calculating area for irregularly shaped lots, specifically triangular parcels. Real estate appraisers must be proficient in geometric calculations since land parcels come in various shapes beyond simple rectangles. The question combines geometric area calculation with unit pricing, which is a common valuation method for land. Understanding how to properly apply the triangular area formula and multiply by a per-square-foot price is essential for accurate land valuation.
Background Knowledge
Appraisers must master basic geometric formulas for calculating areas of various lot shapes, including triangles, rectangles, trapezoids, and irregular polygons. The triangular area formula (base × height ÷ 2) is fundamental, and unit pricing (price per square foot) is a standard method for valuing raw land.
Real-World Application
Triangular lots are common in real estate, especially corner lots, cul-de-sac properties, or parcels created by irregular street patterns. Appraisers must accurately calculate these areas for assessment purposes, highest and best use analysis, and comparison with rectangular lots in the market.
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