An appraiser is analyzing an irregular-shaped lot. The lot can be divided into a rectangle (100' × 80') and a triangle (base 60', height 40'). What is the total area?
Correct Answer
B) 9,200 square feet
Rectangle area: 100 × 80 = 8,000 sq ft. Triangle area: (60 × 40) ÷ 2 = 1,200 sq ft. Total: 8,000 + 1,200 = 9,200 square feet.
Why This Is the Correct Answer
Option B correctly applies the area formulas for both geometric shapes and adds them together. The rectangle area is calculated as length × width (100 × 80 = 8,000 sq ft), and the triangle area uses the formula base × height ÷ 2 (60 × 40 ÷ 2 = 1,200 sq ft). The total area is the sum of both shapes: 8,000 + 1,200 = 9,200 square feet. This demonstrates proper geometric decomposition and mathematical calculation.
Why the Other Options Are Wrong
Option A: 8,000 square feet
This represents only the rectangular portion (8,000 sq ft) and fails to include the triangular area, resulting in an incomplete calculation of the total lot size.
Option C: 1,200 square feet
This represents only the triangular portion (1,200 sq ft) and ignores the much larger rectangular area, severely underestimating the total lot size.
Option D: 10,400 square feet
This appears to incorrectly calculate the triangle area as 60 × 40 = 2,400 sq ft (forgetting to divide by 2), then adding it to the rectangle: 8,000 + 2,400 = 10,400 sq ft.
DART Method
D-Decompose the shape, A-Apply correct formulas (Rectangle = L×W, Triangle = B×H÷2), R-Run the calculations, T-Total all areas together
How to use: When you see an irregular lot, immediately think DART: break it down, apply the right formulas, calculate each piece, then add them all up for the total area
Exam Tip
Always double-check that you're using the correct formula for triangles (don't forget to divide by 2) and verify that your final answer includes ALL geometric components of the irregular shape
Common Mistakes to Avoid
- -Forgetting to divide by 2 when calculating triangle area
- -Only calculating one geometric shape instead of adding all components
- -Mixing up length and width measurements or base and height for triangles
Concept Deep Dive
Analysis
This question tests the fundamental skill of calculating areas for irregular-shaped properties, which is essential in real estate appraisal. Appraisers frequently encounter lots that cannot be measured as simple rectangles and must break them down into basic geometric shapes. The ability to decompose complex shapes into rectangles, triangles, and other basic forms is crucial for accurate property valuation. This skill directly impacts the appraiser's ability to determine land value, which is a significant component of overall property value.
Background Knowledge
Appraisers must master basic geometric formulas: rectangle area = length × width, triangle area = (base × height) ÷ 2, and understand how to decompose irregular shapes into these basic forms. Property boundaries often create complex shapes that require breaking down into calculable components for accurate area determination.
Real-World Application
Appraisers regularly encounter corner lots, flag lots, or properties with unusual boundaries that require geometric decomposition to determine accurate square footage for comparable sales analysis and land valuation
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?
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