A site measuring 150 feet by 200 feet contains how many square feet?
Correct Answer
A) 30,000 square feet
Why this is correct: The area of a rectangular site is calculated as length multiplied by width. Here, 150 feet * 200 feet = 30,000 square feet. Why the other choices are wrong: "75,000 square feet" is wrong; it results from incorrectly adding dimensions (150+200=350, then 350*200?). "350 square feet" is wrong; it results from adding the sides (150+200). "700 square feet" is wrong; it results from calculating the perimeter (2*150 + 2*200 = 700). Exam tip: For area, always multiply the two dimensions. For perimeter, add all sides.
Why This Is the Correct Answer
Option A is correct because area is calculated by multiplying length times width. With dimensions of 150 feet × 200 feet, the calculation is straightforward: 150 × 200 = 30,000 square feet. This represents the total area of the rectangular site. The calculation follows the basic geometric formula for the area of a rectangle, which is fundamental to real estate measurements.
Why the Other Options Are Wrong
Option B: 75,000 square feet
Option B (350 square feet) appears to be the result of adding the dimensions rather than multiplying them (150 + 200 = 350). This is a common error where students confuse perimeter calculation with area calculation. Adding dimensions gives perimeter, not area.
Option C: 350 square feet
Option C (700 square feet) is double the sum of the dimensions (2 × 350 = 700), which might result from calculating perimeter (2 × length + 2 × width = 2 × 150 + 2 × 200 = 700). This confuses the perimeter formula with area calculation and represents a fundamental misunderstanding of geometric measurements.
Option D: 700 square feet
Option D (75,000 square feet) is 2.5 times the correct answer, suggesting a calculation error or misreading of the dimensions. This could result from incorrectly multiplying one dimension by itself or adding an extra digit during calculation.
L × W = Area
Remember 'Length times Width equals Area' or use the acronym 'LWA' (Length × Width = Area). Visualize a rectangle being filled with square tiles - you need length times width tiles to fill it completely.
How to use: When you see site 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.).
Exam Tip
Double-check your multiplication by estimating: 150 × 200 is close to 150 × 200 = 30,000. If your calculator shows a very different number, recalculate to catch input errors.
Common Mistakes to Avoid
- -Adding dimensions instead of multiplying (calculating perimeter instead of area)
- -Confusing linear feet with square feet in the final answer
- -Making arithmetic errors when multiplying large numbers
Concept Deep Dive
Analysis
This question tests the fundamental mathematical skill of calculating area, which is essential for real estate appraisal. Area calculations are used throughout appraisal practice for determining site size, building square footage, and calculating various ratios like floor area ratio (FAR) and building coverage ratio. The formula for rectangular area is simply length × width, and this basic calculation forms the foundation for more complex appraisal computations. Understanding area calculations is critical because property values, zoning compliance, and development potential all depend on accurate square footage measurements.
Background Knowledge
Area calculation requires understanding that area measures two-dimensional space and is expressed in square units. For rectangles and squares, area equals length multiplied by width, while perimeter is the distance around the outside edge.
Real-World Application
Appraisers use area calculations daily to determine lot sizes for zoning compliance, calculate building coverage ratios, determine floor area ratios for development projects, and verify property descriptions in deeds and surveys.
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