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Difficulty: MediumRectangular Area Applications

A roofing crew is applying a waterproof liquid coating to a flat, rectangular building roof that is 90 feet90\text{ feet} long and 60 feet60\text{ feet} wide. If the coating material costs $12\$12 per square yard, what is the total cost to coat the entire roof?

  1. A
    $1,200\$1,200
  2. $7,200\$7,200Answer
  3. C
    $21,600\$21,600
  4. D
    $64,800\$64,800

Answer

The total cost to coat the entire roof is $7,200\$7,200.
To find the total cost, the area must be calculated in square yards because the price is given per square yard. Since 3 feet=1 yard3\text{ feet} = 1\text{ yard}, the dimensions of the roof are 30 yards30\text{ yards} by 20 yards20\text{ yards}. The area is 30×20=600 square yards30 \times 20 = 600\text{ square yards}. Multiplying this area by the $12\$12 cost per square yard yields $7,200\$7,200.

Step-by-Step Solution

1
Convert the length and width of the roof from feet to yards.
Length = 30 yards30\text{ yards}, Width = 20 yards20\text{ yards}.
The cost of the coating is given per square yard, so it is most efficient to work with linear dimensions in yards (3 feet=1 yard3\text{ feet} = 1\text{ yard}).
2
Calculate the total area of the roof in square yards.
30 yards×20 yards=600 square yards30\text{ yards} \times 20\text{ yards} = 600\text{ square yards}.
The area of a rectangle is found by multiplying its length by its width.
3
Multiply the total area by the cost per square yard.
600 sq yd×$12/sq yd=$7,200600\text{ sq yd} \times \$12\text{/sq yd} = \$7,200.
This determines the final material cost required to cover the entire area.

Key Concept

Calculating rectangular area and applying proper unit conversions between square feet and square yards to determine total cost.
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Topics

Rectangular Area Applications

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