A triangular lot has a base of 120 feet and a height of 80 feet. What is the area in square feet?
Correct Answer
B) 4,800 square feet
Area of a triangle is ½ × base × height. ½ × 120 × 80 = 4,800 square feet.
Why This Is the Correct Answer
Option B correctly applies the triangle area formula: Area = ½ × base × height. Substituting the given values: ½ × 120 feet × 80 feet = ½ × 9,600 = 4,800 square feet. This formula works for any triangle when you know the base and the perpendicular height to that base. The calculation is straightforward: multiply base times height, then divide by 2.
Why the Other Options Are Wrong
Option A: 9,600 square feet
This represents the full rectangle area (120 × 80 = 9,600) without applying the ½ factor required for triangles. This is exactly double the correct answer, indicating the student forgot that a triangle is half the area of a rectangle with the same base and height.
Option C: 200 square feet
This appears to be the result of adding base plus height (120 + 80 = 200), which is completely incorrect for area calculation. Area requires multiplication of dimensions, not addition, and this shows a fundamental misunderstanding of geometric principles.
Option D: 400 square feet
This might result from incorrectly dividing the perimeter or using some other flawed calculation method. It's far too small for the given dimensions and doesn't follow any logical geometric formula for the triangle area.
Half-Base-Height Triangle Rule
Remember 'HBH' - Half of Base times Height. Visualize a triangle as half of a rectangle that's been cut diagonally, so you always need to take half of the base × height calculation.
How to use: When you see a triangular lot question, immediately think 'HBH' and write down: ½ × base × height = ? This prevents forgetting the crucial ½ factor that distinguishes triangles from rectangles.
Exam Tip
Always double-check triangle calculations by asking: 'Is my answer exactly half of what base × height would be?' This catches the most common error of forgetting the ½ factor.
Common Mistakes to Avoid
- -Forgetting the ½ factor and calculating base × height
- -Adding base plus height instead of multiplying
- -Confusing perimeter calculation with area calculation
Concept Deep Dive
Analysis
This question tests fundamental geometric area calculation skills essential for real estate appraisers who must accurately measure and calculate property areas. Triangular lots are common in real estate, especially in subdivisions with irregular boundaries or corner properties. The ability to quickly and accurately calculate triangular areas is crucial for determining property values, as land area directly impacts market value. Understanding basic geometric formulas allows appraisers to handle various lot shapes they encounter in practice.
Background Knowledge
Real estate appraisers must master basic geometric formulas to calculate areas of irregularly shaped lots. The triangle area formula (½ × base × height) is fundamental because many properties have triangular sections or can be divided into triangular components for easier calculation.
Real-World Application
Appraisers frequently encounter triangular lots in cul-de-sacs, pie-shaped corner lots, or irregularly subdivided properties. Accurate area calculation is essential for the cost approach and for comparing properties on a per-square-foot basis.
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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