An irregular lot consists of a rectangle (100' × 150') and a triangle (base 100', height 50'). What is the total area in acres?
Correct Answer
B) 0.42 acres
Rectangle: 100 × 150 = 15,000 sq ft. Triangle: (100 × 50) ÷ 2 = 2,500 sq ft. Total: 17,500 sq ft ÷ 43,560 sq ft/acre = 0.40 acres.
Why This Is the Correct Answer
There appears to be an error in the provided explanation. The correct calculation shows: Rectangle = 100 × 150 = 15,000 sq ft, Triangle = (100 × 50) ÷ 2 = 2,500 sq ft, Total = 17,500 sq ft. Converting to acres: 17,500 ÷ 43,560 = 0.4016 acres, which rounds to 0.40 acres. However, the question states B (0.42 acres) is correct, which appears to be inconsistent with the mathematical calculation.
Why the Other Options Are Wrong
Option A: 0.40 acres
Option A shows 0.40 acres, which actually matches the correct mathematical calculation of 17,500 ÷ 43,560 = 0.4016 acres
Option C: 17,500 square feet
Option C gives the answer in square feet (17,500) rather than acres as requested in the question, even though the square footage calculation is correct
Option D: 0.35 acres
Option D (0.35 acres) is too low and would represent only 15,246 square feet when converted back, missing significant area
RATS Method
RATS: Rectangle (L×W), Add Triangle (B×H÷2), Total square feet, Subtract from 43,560 (divide by 43,560 for acres)
How to use: When you see irregular lots, immediately think RATS - identify each shape, calculate areas separately, add them together, then convert using 43,560
Exam Tip
Always double-check your unit conversion - questions often include both square feet and acre options to test if you completed the conversion step
Common Mistakes to Avoid
- -Forgetting to divide triangle area by 2
- -Not converting square feet to acres when requested
- -Adding areas incorrectly when combining shapes
Concept Deep Dive
Analysis
This question tests the fundamental skill of calculating irregular lot areas by breaking them into basic geometric shapes. Real estate appraisers must frequently determine property areas for valuation purposes, especially when dealing with non-standard lot configurations. The problem requires calculating areas of both rectangular and triangular sections, then converting the total from square feet to acres. This type of calculation is essential for determining land value and ensuring accurate property assessments.
Background Knowledge
Appraisers must know basic geometric formulas: rectangle area = length × width, triangle area = (base × height) ÷ 2. The conversion factor of 43,560 square feet per acre is critical for real estate calculations and must be memorized.
Real-World Application
Appraisers encounter irregular lots frequently in subdivisions, corner properties, and rural parcels where natural boundaries create non-rectangular shapes requiring precise area calculations for accurate 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?
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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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