What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
Correct Answer
D) 4,800 square feet
Why this is correct: The area of a triangle is (base × height) ÷ 2. Calculation: (120 feet × 80 feet) ÷ 2 = 9,600 square feet ÷ 2 = 4,800 square feet. Why the other choices are wrong: "400 square feet" might come from misplacing the decimal. "9,600 square feet" is the base × height product before dividing by 2. "200 square feet" is not supported by the numbers. Exam tip: For triangle area, remember 'half of base times height.' Don't forget to divide by 2.
Why This Is the Correct Answer
Option A is correct because it properly applies the triangle area formula: Area = (base × height) ÷ 2. With a base of 120 feet and height of 80 feet, the calculation is (120 × 80) ÷ 2 = 9,600 ÷ 2 = 4,800 square feet. This formula accounts for the fact that a triangle is exactly half the area of a rectangle with the same base and height dimensions. The division by 2 is the critical step that distinguishes triangle area calculations from rectangle area calculations.
Why the Other Options Are Wrong
Option A: 400 square feet
Option A (400 square feet) seems to result from an unclear calculation method, possibly dividing the sum of base and height by 2 [(120 + 80) ÷ 2 = 100] and then applying some other incorrect operation. This represents a complete misapplication of geometric formulas.
Option B: 9,600 square feet
Option B (9,600 square feet) represents the common error of forgetting to divide by 2, essentially calculating the area as if it were a rectangle (120 × 80 = 9,600). This mistake occurs when someone multiplies base times height but fails to apply the triangle-specific division by 2.
Option C: 200 square feet
Option C (200 square feet) appears to result from adding the base and height (120 + 80 = 200), which is completely incorrect for area calculations. This represents a fundamental misunderstanding of how area is calculated and confuses linear measurement with area measurement.
Triangle Half-Rectangle Rule
Remember 'BH/2' - Base times Height divided by 2. Think of it as 'Be Happy, divide by 2' or visualize that a triangle is exactly half of a rectangle, so you always cut the rectangle area in half.
How to use: When you see any triangle area question, immediately write 'BH/2' at the top of your scratch work, then identify which measurements are the base and height, multiply them, and divide by 2.
Exam Tip
Always double-check that you divided by 2 for triangle calculations - if your answer matches one of the larger options, you likely forgot this crucial step.
Common Mistakes to Avoid
- -Forgetting to divide by 2 and calculating as a rectangle
- -Adding base and height instead of multiplying
- -Confusing which measurements represent the base and height in the triangle
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation for determining the area of a triangular lot, which is essential for real estate appraisers when calculating property sizes and values. The triangle area formula (base × height ÷ 2) is one of the most basic yet critical calculations in real estate appraisal. Understanding this concept is crucial because many properties have irregular shapes, including triangular lots, and accurate area calculations directly impact property valuations. Appraisers must be able to quickly and accurately perform these calculations to determine square footage for comparison purposes and valuation analysis.
Background Knowledge
Real estate appraisers must master basic geometric formulas to calculate property areas accurately, as lot sizes directly impact property values and comparability analysis. The triangle area formula (base × height ÷ 2) is fundamental because many properties have irregular shapes that can be broken down into triangular components for calculation purposes.
Real-World Application
Appraisers frequently encounter triangular lots, especially corner lots, pie-shaped lots, or irregularly shaped properties that must be broken into geometric components. Accurate area calculations are essential for determining price per square foot comparisons and ensuring proper valuation methodology.
More Property Description Questions
A building cost $2,500,000 to construct 8 years ago. Using straight-line depreciation over a 40-year life, what is the current depreciated value?
The following sale prices were recorded: $245,000, $250,000, $250,000, $255,000, $280,000. What is the mode?
A property has a replacement cost of $1,800,000. Physical deterioration is estimated at $200,000, functional obsolescence at $150,000, and external obsolescence at $100,000. What is the depreciated value using the breakdown method?
What is the present value of $150,000 to be received in 5 years, assuming a discount rate of 8%?
A triangular lot has a base of 100 feet and a height of 80 feet. What is the area in square feet?
An irregular lot can be divided into a rectangle (100' × 80') and a triangle (base 60', height 40'). What is the total area in acres?
A property has a net operating income of $85,000 and annual debt service of $68,000. What is the debt coverage ratio?
A warehouse has interior dimensions of 120 feet × 80 feet × 20 feet high. What is the volume in cubic feet?
A property is purchased for $500,000 with a loan of $400,000. What is the loan-to-value ratio?
A property sold for $400,000 with annual gross rent of $40,000. What is the gross rent multiplier?
People Also Study
Real Estate Market
13.6% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Income Approach
8.2% of exam
Related Tools
Previous Question
A comparable sale requires a +$15,000 adjustment for location and a -$8,000 adjustment for condition. If the comparable sold for $325,000, what is the adjusted sale price?
Next Question
An office building generates $180,000 in net operating income and has a capitalization rate of 8.5%. What is the indicated value?