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Difficulty: MediumRectangular Area Applications

A landscaper is installing sod in a rectangular backyard that is 4545 feet long and 3030 feet wide. If the sod costs $6.00\$6.00 per square yard, what is the total cost of the sod for the backyard?

  1. A
    $300\$300
  2. $900\$900Answer
  3. C
    $2,700\$2,700
  4. D
    $8,100\$8,100

Answer

The total cost of the sod for the backyard is $900\$900.
The correct answer is found by determining the area in square yards and multiplying by the unit price. Converting the dimensions first gives 1515 yards by 1010 yards, yielding an area of 150150 square yards. Multiplying 150150 by $6.00\$6.00 gives a total cost of $900\$900.

Step-by-Step Solution

1
Convert the dimensions of the rectangular backyard from feet to yards.
Length = 45÷3=1545 \div 3 = 15 yards; Width = 30÷3=1030 \div 3 = 10 yards.
Since the cost is given per square yard, it is most efficient to calculate the area in square yards by first converting the linear dimensions.
2
Calculate the area of the backyard in square yards.
15 yards×10 yards=150 square yards15 \text{ yards} \times 10 \text{ yards} = 150 \text{ square yards}.
The area of a rectangle is found by multiplying its length by its width.
3
Calculate the total cost of the sod.
150 square yards×$6.00/square yard=$900150 \text{ square yards} \times \$6.00/\text{square yard} = \$900.
Multiplying the total area in square yards by the cost per square yard gives the final total cost.

Key Concept

Calculating rectangular area and applying appropriate unit conversions to estimate total cost.

Alternative Method

You can also calculate the area in square feet first (45×30=1,35045 \times 30 = 1,350 sq ft), then divide by 99 to convert to square yards (1,350÷9=1501,350 \div 9 = 150 sq yds), and finally multiply by the cost per square yard.
Estimated Time:1m 30s
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Topics

Rectangular Area Applications

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