A site consists exactly of two nonoverlapping rectangles, 100 ft by 150 ft and 120 ft by 30 ft. What is their total area in square feet?
Correct Answer
C) 18,600 square feet
Total area=100 ft×150 ft+120 ft×30 ft=15000+3600=18600 square feet. Common errors: leaving out the second rectangle gives 15,000 square feet; reporting only the second rectangle gives 3,600 square feet; multiplying the combined widths by the combined lengths gives 39,600 square feet.
Why This Is the Correct Answer
Option C is correct because the total area is 100 ft x 150 ft + 120 ft x 30 ft = 15,000 + 3,600 = 18,600 square feet. Because the rectangles do not overlap, their separate areas simply add.
Why the Other Options Are Wrong
Option A: 3,600 square feet
Option A is wrong because 3,600 square feet is only the second rectangle, 120 x 30 = 3,600. The first rectangle's 15,000 square feet must be added for a total of 18,600 square feet.
Option B: 15,000 square feet
Option B is wrong because 15,000 square feet is only the first rectangle, 100 x 150 = 15,000, leaving out the second rectangle. Adding 120 x 30 = 3,600 gives 18,600 square feet.
Option D: 39,600 square feet
Option D is wrong because 39,600 square feet comes from multiplying the combined widths by the combined lengths, (100 + 120) x (150 + 30) = 39,600. Separate rectangles must be multiplied individually and then added: 15,000 + 3,600 = 18,600 square feet.
Split, multiply, then add
Break the site into separate shapes, multiply length by width for each one, then add the results instead of multiplying sums of sides.
How to use: Use this for any irregular site made of nonoverlapping rectangles.
Exam Tip
Compute each shape's area on its own before adding, and check that your answer exceeds each individual piece.
Common Mistakes to Avoid
- -Reporting only one of the rectangles
- -Multiplying the combined widths by the combined lengths
- -Adding the side lengths instead of multiplying them
Concept Deep Dive
Analysis
This question tests calculating the area of a site made of two nonoverlapping rectangles. Each rectangle's area is found by multiplying its own length and width, and the two areas are then added together.
Background Knowledge
Irregular sites are often measured by breaking them into simple shapes such as rectangles and triangles, calculating each area and adding them. Area is expressed in square feet or acres, with 1 acre equal to 43,560 square feet. Accurate site area supports the site description and any site value analysis.
Real-World Application
An appraiser has an L-shaped lot from a plat showing a 100 by 150 foot main area and a 120 by 30 foot strip. The appraiser calculates 15,000 plus 3,600 for a site area of 18,600 square feet, about 0.43 acres.
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