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 (base × height) ÷ 2. (120 feet × 80 feet) ÷ 2 = 4,800 square feet.
Why This Is the Correct Answer
Option B correctly 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 demonstrates proper understanding of the geometric principle that a triangle's area is exactly half the area of a rectangle with the same base and height dimensions.
Why the Other Options Are Wrong
Option A: 9,600 square feet
This represents the full rectangular area (120 × 80 = 9,600) without dividing by 2, which is the most common error when calculating triangle area.
Option C: 200 square feet
This appears to be the result of adding base and height (120 + 80 = 200) rather than using the proper area formula, showing confusion between perimeter-type calculations and area calculations.
Option D: 19,200 square feet
This is double the rectangular area (9,600 × 2 = 19,200), suggesting a fundamental misunderstanding of the triangle area formula by multiplying instead of dividing by 2.
Triangle Half-Cut Method
Remember 'Cut the Rectangle in HALF' - visualize folding a rectangle diagonally and cutting it, leaving exactly half the original area. The acronym 'BH/2' (Base × Height ÷ 2) sounds like 'Be Half' to reinforce that triangles are half of rectangles.
How to use: When you see triangle area problems, immediately think 'Be Half' and write down BH/2, then substitute the given measurements and calculate step by step.
Exam Tip
Always double-check triangle calculations by asking yourself: 'Is my answer exactly half of what base × height would be?' This quick verification catches the most common error.
Common Mistakes to Avoid
- -Forgetting to divide by 2 and using the full rectangular area
- -Adding base and height instead of multiplying
- -Multiplying by 2 instead of dividing by 2
Concept Deep Dive
Analysis
This question tests the fundamental geometric calculation for determining the area of triangular lots, which is essential knowledge for real estate appraisers. Triangular lots are common in real estate, especially at intersections, cul-de-sacs, or irregularly shaped developments. The formula for triangle area (base × height ÷ 2) is one of the most basic area calculations appraisers must master. Understanding this concept is crucial because lot area directly impacts property valuation, and incorrect calculations can lead to significant appraisal errors.
Background Knowledge
Real estate appraisers must be proficient in basic geometric area calculations since property value is often determined per square foot or acre. Triangle area calculations are particularly important for irregularly shaped lots, partial takings in eminent domain cases, and corner properties.
Real-World Application
An appraiser valuing a corner lot at a busy intersection needs to calculate the triangular portion created by a street widening project to determine the remaining buildable area and adjust the property's market value accordingly.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
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