An irregularly shaped lot can be divided into a rectangle (100' × 150') and a triangle (base 80', height 60'). What is the total area in square feet?
Correct Answer
D) 17,400 square feet
Why this is correct: Calculate each shape's area separately. Rectangle: 100 ft × 150 ft = 15,000 sq ft. Triangle: area = (base × height) ÷ 2 = (80 ft × 60 ft) ÷ 2 = 2,400 sq ft. Total: 15,000 + 2,400 = 17,400 sq ft. Why the other choices are wrong: "12,600 square feet" might incorrectly add rectangle perimeter or miscalculate triangle area. "15,000 square feet" only counts the rectangle. "2,400 square feet" only counts the triangle. Exam tip: For composite shapes, always break them into simple rectangles and triangles, calculate each area, then sum.
Why This Is the Correct Answer
Option A correctly applies the area formulas for both geometric shapes and adds them together. The rectangle area is calculated as length × width (100' × 150' = 15,000 sq ft), and the triangle area uses the formula base × height ÷ 2 (80' × 60' ÷ 2 = 2,400 sq ft). The total area is the sum of both components: 15,000 + 2,400 = 17,400 square feet. This demonstrates proper geometric decomposition and accurate mathematical computation.
Why the Other Options Are Wrong
DART Method
D-ivide the shape, A-rea formulas (Rectangle = L×W, Triangle = B×H÷2), R-ecord each calculation, T-otal them up
How to use: When you see an irregular lot, immediately think DART: break it into basic shapes, apply the correct area formula to each piece, write down each result, then add all areas together for the total.
Exam Tip
Always double-check that you're adding ALL the component areas together - a common exam mistake is calculating each shape correctly but forgetting to sum them for the final answer.
Common Mistakes to Avoid
- -Forgetting to divide by 2 when calculating triangle area
- -Only calculating one geometric component instead of adding all parts
- -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 irregularly shaped properties, which is essential in real estate appraisal. Appraisers must be able to break down complex lot shapes into basic geometric forms (rectangles, triangles, circles) and calculate each area separately. The key concept is geometric decomposition - dividing an irregular shape into recognizable geometric components whose areas can be calculated using standard formulas. This skill is critical for determining land value, which often depends on usable square footage and lot size.
Background Knowledge
Real estate appraisers must master basic geometry to calculate property areas, as land value is often determined by square footage. Standard formulas include: rectangle (length × width), triangle (base × height ÷ 2), and circle (π × radius²).
Real-World Application
Appraisers regularly encounter irregularly shaped lots, especially corner properties, flag lots, or parcels with natural boundaries like rivers. Accurate area calculation directly impacts property valuation since land is often valued per square foot.
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