A triangular lot has a base of 100 feet and a height of 80 feet. What is the area in square feet?
Correct Answer
B) 4,000 square feet
Area of a triangle is calculated as ½ × base × height. ½ × 100 feet × 80 feet = 4,000 square feet.
Why This Is the Correct Answer
Option B is correct because it properly applies the triangle area formula: Area = ½ × base × height. Substituting the given values: Area = ½ × 100 feet × 80 feet = ½ × 8,000 = 4,000 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 formula is universally applicable to all triangles when you have the base and perpendicular height measurements.
Why the Other Options Are Wrong
Option A: 8,000 square feet
Option A represents the full rectangular area (100 × 80 = 8,000) without applying the ½ factor required for triangular area calculation, essentially calculating the area as if it were a rectangle instead of a triangle.
Option C: 180 square feet
Option C appears to be the simple addition of base plus height (100 + 80 = 180), which is completely incorrect for area calculation and represents a fundamental misunderstanding of geometric formulas.
Option D: 360 square feet
Option D seems to be double the sum of base and height (2 × 180 = 360), which has no mathematical relationship to triangle area calculation and represents an incorrect approach to the problem.
Half-Base-Height Triangle Rule
Remember 'HBH' - Half × Base × Height. Visualize cutting a rectangle diagonally in half - the triangle is exactly half the rectangle's area.
How to use: When you see a triangular lot question, immediately think 'HBH' and visualize cutting a rectangle in half diagonally. This reminds you to multiply base × height, then divide by 2 (or multiply by ½).
Exam Tip
Always double-check that you've applied the ½ factor when calculating triangle areas - forgetting this step and calculating the full rectangular area is the most common error on triangle area questions.
Common Mistakes to Avoid
- -Forgetting to multiply by ½ and calculating the full rectangular area instead
- -Adding base and height instead of multiplying them
- -Confusing which measurements represent the base and height in the triangle
Concept Deep Dive
Analysis
This question tests fundamental geometric calculation skills essential for real estate appraisers who must accurately determine property areas for valuation purposes. Triangular lots are common in real estate, especially in subdivisions with irregular boundaries, corner properties, or areas with natural constraints. The ability to calculate area using the basic triangle formula (½ × base × height) is a core competency that appraisers use daily when measuring and valuing irregularly shaped properties. Understanding this formula is crucial because property value is often directly correlated with usable land area, making accurate area calculations essential for proper valuation.
Background Knowledge
Real estate appraisers must be proficient in basic geometric calculations to determine property areas for various lot shapes including triangular, rectangular, and irregular parcels. The triangle area formula (½ × base × height) is fundamental because many properties have triangular sections or can be broken down into triangular components for calculation purposes.
Real-World Application
Appraisers frequently encounter triangular lots in corner properties, pie-shaped lots in cul-de-sacs, or irregularly shaped parcels that must be broken into triangular sections for accurate area calculation and subsequent valuation 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?
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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?
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