A triangular lot has a base of 100 feet and a height of 80 feet. What is the area in square feet?
Correct Answer
D) 4,000 square feet
Why this is correct: The area of any triangle is given by the formula: Area = (1/2) * base * height. Applying the given numbers: Area = (1/2) * 100 feet * 80 feet. First, multiply base and height: 100 * 80 = 8,000. Then, multiply by 1/2 (or divide by 2): 8,000 / 2 = 4,000 square feet. Why the other choices are wrong: 8,000 square feet is the result of forgetting to multiply by 1/2 (using base * height only). 180 square feet incorrectly adds the dimensions (100 + 80). 360 square feet appears to be an unrelated calculation, possibly a perimeter estimate. Exam tip: For triangle area, always remember the 'half.' A common trap is to give the rectangle area (base * height) as an option.
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
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.
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