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Difficulty: MediumRectangular Area Applications

A university is installing artificial turf on an indoor practice facility. The rectangular facility measures 120 feet120\text{ feet} in length and 60 feet60\text{ feet} in width. Inside the facility, there are two identical rectangular equipment zones, each measuring 30 feet30\text{ feet} long and 15 feet15\text{ feet} wide, which will remain bare concrete and will not be covered with turf. If the artificial turf costs $24\$24 per square yard, what is the total cost, in dollars, of the artificial turf needed for the facility?

Answer: 16800 dollars

Answer

16800
The correct answer is found by calculating the total area of the facility (7,200 sq ft7,200\text{ sq ft}), subtracting the area of the two equipment zones (900 sq ft900\text{ sq ft}), converting the remaining area (6,300 sq ft6,300\text{ sq ft}) from square feet to square yards by dividing by 9 (700 sq yd700\text{ sq yd}), and finally multiplying by the cost per square yard (24)toget24) to get 16,800.

Step-by-Step Solution

1
Calculate the total area of the facility.
120×60=7,200 sq ft120 \times 60 = 7,200\text{ sq ft}
To establish the maximum possible area before exclusions.
2
Calculate the area of the two equipment zones that will not be turfed.
2×(30×15)=900 sq ft2 \times (30 \times 15) = 900\text{ sq ft}
The two zones are bare concrete, so their combined area must be subtracted from the total.
3
Subtract the equipment zones from the total facility area.
7,200−900=6,300 sq ft7,200 - 900 = 6,300\text{ sq ft}
To find the actual area that requires artificial turf.
4
Convert the turfed area from square feet to square yards.
6,300÷9=700 sq yd6,300 \div 9 = 700\text{ sq yd}
There are 9 square feet in one square yard (3 ft×3 ft3\text{ ft} \times 3\text{ ft}), and the turf is priced per square yard.
5
Calculate the total cost.
700×24=$16,800700 \times 24 = \$16,800
Multiplying the required square yards by the price per square yard gives the final cost.

Key Concept

Calculating area with subtractive regions and converting between square units.
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Topics

Rectangular Area Applications

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