An irregular shaped lot has the following measurements: Side A = 100 feet, Side B = 150 feet, Side C = 120 feet, Side D = 180 feet. If the lot can be divided into two rectangles measuring 100' × 150' and 120' × 30', what is the total area?
Correct Answer
A) 18,600 square feet
Rectangle 1: 100' × 150' = 15,000 sq ft. Rectangle 2: 120' × 30' = 3,600 sq ft. Total area = 15,000 + 3,600 = 18,600 square feet.
Why This Is the Correct Answer
Option A is correct because it properly calculates the area of both rectangles and adds them together. Rectangle 1 has dimensions 100' × 150' = 15,000 square feet, and Rectangle 2 has dimensions 120' × 30' = 3,600 square feet. The total area is the sum of both rectangles: 15,000 + 3,600 = 18,600 square feet. This demonstrates the proper method for finding irregular lot areas by decomposition into simpler shapes.
Why the Other Options Are Wrong
Option B: 15,000 square feet
Option B represents only the area of the first rectangle (100' × 150' = 15,000 sq ft) and fails to include the second rectangle's area, resulting in an incomplete calculation of the total lot area.
Option C: 3,600 square feet
Option C represents only the area of the second rectangle (120' × 30' = 3,600 sq ft) and ignores the first rectangle's area, providing only a partial calculation of the total lot area.
Option D: 550 square feet
Option D appears to be the sum of the perimeter measurements (100 + 150 + 120 + 180 = 550 feet), which confuses linear measurement with area calculation and represents a fundamental misunderstanding of the question.
DIVIDE and MULTIPLY
D.I.V.I.D.E. - Divide Irregular shapes, Visualize rectangles, Individual calculations, Determine each area, Execute addition. Remember: Break it down, calculate each piece, add them up!
How to use: When you see an irregular lot problem, immediately think 'DIVIDE' - look for how the shape can be broken into rectangles or triangles, calculate each piece separately using length × width, then add all pieces together for the total.
Exam Tip
Always double-check that you're adding ALL the component areas together - a common exam mistake is calculating individual rectangles correctly but forgetting to sum them, leading to partial answers.
Common Mistakes to Avoid
- -Calculating only one rectangle's area instead of both
- -Adding perimeter measurements instead of calculating area
- -Multiplying all four given side measurements together incorrectly
Concept Deep Dive
Analysis
This question tests the fundamental skill of calculating irregular lot areas by decomposing complex shapes into simpler geometric forms. The key concept is that irregular lots can often be broken down into rectangles, triangles, or other basic shapes whose areas can be calculated using standard formulas. This approach is essential in real estate appraisal because properties rarely have perfectly regular boundaries. The question provides the individual side measurements but then gives you the decomposition into two rectangles, requiring you to calculate each area separately and sum them for the total.
Background Knowledge
Real estate appraisers must be proficient in calculating areas of irregular lots since most properties don't have perfect rectangular shapes. The standard approach is to divide complex shapes into simpler geometric forms like rectangles, triangles, or trapezoids, calculate each area separately, then sum them for the total area.
Real-World Application
In practice, appraisers frequently encounter irregular lots, especially in older neighborhoods or areas with natural boundaries like rivers or hills. They use surveyor drawings and legal descriptions to break down complex shapes into measurable components, ensuring accurate square footage for valuation purposes.
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An irregular lot has the following dimensions: Side A = 120 feet, Side B = 200 feet, Side C = 150 feet, Side D = 180 feet. If this lot can be divided into a rectangle (120' × 180') and a triangle with base 80 feet and height 150 feet, what is the total area?
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