An irregular shaped lot has the following measurements: Side A = 100 ft, Side B = 150 ft, Side C = 80 ft, Side D = 120 ft. If the lot can be divided into two rectangles of 100×80 and 50×120, what is the total area?
Correct Answer
A) 14,000 square feet
Total area = Area of rectangle 1 + Area of rectangle 2. (100 × 80) + (50 × 120) = 8,000 + 6,000 = 14,000 square feet.
Why This Is the Correct Answer
Option A is correct because it properly applies the decomposition method for calculating irregular lot area. The problem states the lot can be divided into two rectangles: one measuring 100×80 feet and another measuring 50×120 feet. Using the formula Area = length × width, the first rectangle equals 8,000 square feet and the second equals 6,000 square feet. Adding these together gives the total area of 14,000 square feet.
Why the Other Options Are Wrong
Option B: 450 square feet
Option B (450 square feet) appears to be the result of adding the perimeter measurements rather than calculating area, or possibly adding the dimensions incorrectly without applying the area formula.
Option C: 8,000 square feet
Option C (8,000 square feet) represents only the area of the first rectangle (100×80) and fails to include the area of the second rectangle (50×120), resulting in an incomplete calculation.
Option D: 6,000 square feet
Option D (6,000 square feet) represents only the area of the second rectangle (50×120) and omits the area of the first rectangle (100×80), providing only a partial answer.
DIVIDE and ADD Method
D.I.V.I.D.E. = Divide Irregular shapes, Verify measurements, Identify rectangles, Determine each area, Execute multiplication, ADD all areas together
How to use: When you see an irregular lot problem, immediately think 'DIVIDE and ADD' - first divide the shape into simple rectangles, calculate each area separately, then add them together for the total.
Exam Tip
Always double-check that you've included all component areas when dealing with irregular lots - a common exam mistake is calculating only one portion and forgetting to add the remaining areas.
Common Mistakes to Avoid
- -Calculating only one rectangle's area instead of both
- -Adding perimeter measurements instead of calculating area
- -Confusing length and width measurements when setting up the area calculation
Concept Deep Dive
Analysis
This question tests the fundamental skill of calculating area for irregular lots by decomposing them into simpler geometric shapes. Real estate appraisers frequently encounter properties with irregular boundaries that cannot be measured as a single rectangle or square. The key concept is recognizing that complex shapes can be broken down into multiple rectangles, triangles, or other basic geometric forms whose areas can be calculated separately and then summed. This decomposition method is essential for accurate property valuation and land assessment.
Background Knowledge
Appraisers must be proficient in basic geometry and area calculations since property size directly impacts value. Understanding how to decompose irregular shapes into manageable geometric components is essential for accurate lot size determination and subsequent valuation analysis.
Real-World Application
In practice, appraisers use this technique when valuing corner lots, flag lots, or properties with unusual configurations where the total square footage must be calculated for comparison with similar properties or for cost approach valuations.
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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