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?
Correct Answer
B) 27,600 square feet
Rectangle area: 120 × 180 = 21,600 sq ft. Triangle area: (80 × 150) ÷ 2 = 6,000 sq ft. Total area: 21,600 + 6,000 = 27,600 square feet.
Why This Is the Correct Answer
Option B correctly applies the decomposition method by calculating the rectangle area (120 × 180 = 21,600 sq ft) and triangle area using the formula (base × height) ÷ 2 = (80 × 150) ÷ 2 = 6,000 sq ft. The total area is found by adding these components: 21,600 + 6,000 = 27,600 square feet. This demonstrates proper understanding of geometric area calculations and the additive principle for composite shapes.
Why the Other Options Are Wrong
Option A: 21,600 square feet
This represents only the rectangular portion (21,600 sq ft) and fails to include the triangular area, resulting in an incomplete calculation of the total lot area.
Option C: 24,000 square feet
This appears to be the result of incorrectly calculating the triangle area as 80 × 150 ÷ 5 = 2,400, then adding to the rectangle (21,600 + 2,400 = 24,000), showing a fundamental error in triangle area formula.
Option D: 30,600 square feet
This likely results from calculating the triangle area incorrectly as 80 × 150 ÷ 2 = 6,000, but then making an arithmetic error in the final addition, possibly adding 21,600 + 9,000 instead of 21,600 + 6,000.
RAT Method
RAT = Rectangle + Add + Triangle. Remember: Rectangle first (L×W), Add the areas, Triangle last (B×H÷2). The rat runs around the property perimeter, first in rectangles, then through triangular corners.
How to use: When you see an irregular lot problem, immediately think 'RAT' - identify the Rectangle dimensions, plan to Add the areas, and locate the Triangle measurements. This ensures you don't forget any component areas.
Exam Tip
Always double-check that you've accounted for all geometric components of an irregular lot - draw a quick sketch if needed and label each shape's area before adding them together.
Common Mistakes to Avoid
- -Forgetting to divide triangle area by 2
- -Only calculating one geometric component and missing others
- -Using wrong dimensions for triangle base or height
Concept Deep Dive
Analysis
This question tests the appraiser's ability to calculate areas of irregular lots by decomposing them into simpler geometric shapes. Real estate appraisers frequently encounter properties with irregular boundaries that cannot be measured using a single formula. The key skill is recognizing how to break down complex shapes into rectangles, triangles, and other basic geometric forms. This decomposition method is essential for accurate lot valuation and is a fundamental competency tested on appraisal exams.
Background Knowledge
Appraisers must master basic geometric formulas including rectangle area (length × width) and triangle area (base × height ÷ 2). Understanding how to decompose irregular lots into standard geometric shapes is crucial for accurate property measurement and valuation.
Real-World Application
Appraisers regularly encounter irregular lots in subdivisions, corner properties, or parcels with natural boundaries like rivers or hills, requiring decomposition into measurable geometric shapes for accurate square footage calculations in valuation reports.
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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?