A triangular lot has a base of 180 feet and a height of 240 feet. What is the area in square feet?
Correct Answer
A) 21,600 square feet
Area of triangle = ½ × base × height = ½ × 180 × 240 = 21,600 square feet.
Why This Is the Correct Answer
Option A is correct because it properly applies the triangle area formula: Area = ½ × base × height. Substituting the given values: Area = ½ × 180 feet × 240 feet = ½ × 43,200 = 21,600 square feet. This calculation follows the standard geometric principle that a triangle's area is exactly half the area of a rectangle with the same base and height dimensions. The answer demonstrates proper understanding of both the formula and basic arithmetic operations required for real estate calculations.
Why the Other Options Are Wrong
Option B: 43,200 square feet
Option B (43,200) represents the area calculation without applying the ½ factor, essentially calculating base × height as if it were a rectangle rather than a triangle. This is a common error where candidates forget that triangular area is half the area of the corresponding rectangle.
Option C: 10,800 square feet
Option C (10,800) appears to result from incorrectly applying the ½ factor twice or making an arithmetic error in the multiplication process. This could occur from miscalculating ½ × ½ × 180 × 240 or from other computational mistakes.
Option D: 420 square feet
Option D (420) is far too small and likely results from adding the base and height (180 + 240 = 420) rather than using the proper area formula. This represents a fundamental misunderstanding of area calculation versus perimeter-type calculations.
Half-Base-Height Triangle Rule
Remember 'HBH' - Half times Base times Height. Visualize cutting a rectangle diagonally in half to create two identical triangles, reinforcing that triangle area is always half the rectangle area.
How to use: When you see a triangle area problem, immediately think 'HBH' and write down ½ × base × height before substituting numbers. This prevents forgetting the crucial ½ factor that distinguishes triangles from rectangles.
Exam Tip
Always double-check that you've included the ½ factor in triangle calculations - this is the most common error on triangle area questions.
Common Mistakes to Avoid
- -Forgetting the ½ factor and calculating as a rectangle
- -Adding base and height instead of multiplying
- -Applying the ½ factor twice or in the wrong position
Concept Deep Dive
Analysis
This question tests the fundamental geometric skill of calculating triangular lot area, which is essential for real estate appraisers who frequently encounter irregularly shaped properties. The triangle area formula (½ × base × height) is one of the most basic area calculations appraisers must master, as triangular lots are common in subdivisions, corner properties, and irregularly platted land. Understanding this calculation is crucial for accurate property valuation, as land area directly impacts property value. The question specifically tests whether candidates can correctly apply the formula and avoid common computational errors.
Background Knowledge
Real estate appraisers must be proficient in calculating areas for various geometric shapes, with triangular lots being particularly common in urban and suburban developments. The triangle area formula (Area = ½ × base × height) is derived from the fact that any triangle occupies exactly half the space of a rectangle with identical base and height measurements.
Real-World Application
Appraisers frequently encounter triangular lots at street intersections, cul-de-sac properties, or irregularly subdivided land where accurate area calculation directly impacts the property's assessed value and market price per square foot.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
People Also Study
Valuation Principles & Procedures
25% of exam
Property Description & Analysis
20% of exam
Market Analysis & Highest/Best Use
15% of exam
USPAP (Ethics & Standards)
15% of exam
Report Writing & Compliance
10% of exam
Related Tools
Previous Question
A building has an effective age of 15 years and a total economic life of 60 years. Using the age-life method, what is the depreciation percentage?
Next Question
A comparable property sold for $400,000. The subject property has a garage worth $15,000 that the comparable lacks. The subject also lacks a fireplace worth $8,000 that the comparable has. What is the adjusted sale price of the comparable?