A rectangular lot measures 150 feet by 200 feet. What is the area in square feet?
Correct Answer
A) 30,000 square feet
Area of a rectangle is length × width. 150 feet × 200 feet = 30,000 square feet.
Why This Is the Correct Answer
Option A is correct because it properly applies the rectangle area formula: Area = Length × Width. When we multiply 150 feet by 200 feet, we get 30,000 square feet. This calculation follows the fundamental geometric principle that area represents the two-dimensional space enclosed within the boundaries of a shape. The units are correctly expressed as square feet, indicating a two-dimensional measurement.
Why the Other Options Are Wrong
Option B: 350 square feet
Option B (350 square feet) appears to be the result of adding the length and width (150 + 200 = 350) rather than multiplying them. This is a fundamental error that confuses perimeter calculation with area calculation.
Option C: 700 square feet
Option C (700 square feet) represents double the perimeter calculation (2 × (150 + 200) = 700), which is completely incorrect for area measurement. This suggests confusion between area and perimeter formulas.
Option D: 15,000 square feet
Option D (15,000 square feet) appears to be half the correct answer, possibly resulting from dividing one dimension by 2 before multiplying (75 × 200 = 15,000 or 150 × 100 = 15,000). This represents a calculation error or misreading of the given dimensions.
L×W Rectangle Rule
Remember 'Length times Width = Area' with the phrase 'Love Wins Always' where L×W=A. Visualize a rectangular lot as a grid where you count rows (length) times columns (width) to get total squares.
How to use: When you see rectangular dimensions, immediately identify which measurement is length and which is width, then multiply them together. Always check that your answer is in square units (square feet, square yards, etc.) to confirm you calculated area, not perimeter.
Exam Tip
Double-check your calculation by ensuring the answer is reasonable - a 150×200 foot lot should be substantial (30,000 sq ft is about 0.69 acres), not tiny like 350 sq ft.
Common Mistakes to Avoid
- -Adding dimensions instead of multiplying (confusing area with perimeter)
- -Forgetting to use square units in the final answer
- -Misreading or transposing the given dimensions during calculation
Concept Deep Dive
Analysis
This question tests fundamental geometric calculation skills essential for real estate appraisal, specifically the ability to calculate rectangular area. Area calculations are foundational to property valuation as they determine the size of lots, buildings, and other improvements. Understanding how to properly multiply length by width is crucial for appraisers who must accurately measure and calculate property dimensions. This basic skill underlies more complex calculations involving property values, cost approaches, and market comparisons.
Background Knowledge
Real estate appraisers must master basic geometric formulas to calculate property areas, which directly impact property values and assessments. The area formula for rectangles (Area = Length × Width) is fundamental to determining lot sizes, building footprints, and usable space calculations.
Real-World Application
Appraisers use area calculations daily when measuring residential lots, commercial properties, and building footprints. Accurate area measurements are essential for the cost approach to value, comparing properties per square foot, and determining highest and best use of land.
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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