Rectangular Area Applications

22 questions

A hotel director is purchasing custom carpet for a rectangular conference room that measures $45\text{ feet}$ in length and $36\text{ feet}$ in width. The carpet is priced at $\$15$ per square yard. What is the total cost of the carpet needed to completely cover the room?

\$810

\$2,700

\$8,100

\$24,300

Show answer & explanation

Answer: $\$2,700$

Answer

\$2,700

First, the area of the rectangular room is found by multiplying the length and width:

45\text{ feet} \times 36\text{ feet} = 1,620\text{ square feet}

. Next, because the carpet is priced per square yard, the area must be converted. Since

1\text{ square yard}

equals

9\text{ square feet}

, divide the area by 9:

1,620 \div 9 = 180\text{ square yards}

. Finally, multiply the

180\text{ square yards}

by the unit price of

\$15

to get the total cost of

\$2,700

Step-by-Step Solution

Calculate the total area of the room in square feet.

45\text{ feet} \times 36\text{ feet} = 1,620\text{ square feet}

The area formula for a rectangle (length multiplied by width) determines the total floor space to be covered.

Convert the area from square feet to square yards.

1,620 \div 9 = 180\text{ square yards}

The carpet is priced per square yard. Because

1\text{ yard} = 3\text{ feet}

1\text{ square yard} = 3\text{ feet} \times 3\text{ feet} = 9\text{ square feet}

. You must divide by 9.

Calculate the total cost by multiplying the area in square yards by the price per square yard.

180\text{ square yards} \times \$15\text{/square yard} = \$2,700

Multiplying the total required material by the unit price gives the final cost.

Key Concept

Calculating rectangular area and converting between two-dimensional units (square feet to square yards) before applying rates.

Question 22Question →

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

Show answer & explanation

Answer: 16800

Answer

16800

The correct answer is found by calculating the total area of the facility (

7,200\text{ sq ft}

), subtracting the area of the two equipment zones (

900\text{ sq ft}

), converting the remaining area (

6,300\text{ sq ft}

) from square feet to square yards by dividing by 9 (

700\text{ sq yd}

), and finally multiplying by the cost per square yard (

24) to get

16,800.

Step-by-Step Solution

Calculate the total area of the facility.

120 \times 60 = 7,200\text{ sq ft}

To establish the maximum possible area before exclusions.

Calculate the area of the two equipment zones that will not be turfed.

2 \times (30 \times 15) = 900\text{ sq ft}

The two zones are bare concrete, so their combined area must be subtracted from the total.

Subtract the equipment zones from the total facility area.

7,200 - 900 = 6,300\text{ sq ft}

To find the actual area that requires artificial turf.

Convert the turfed area from square feet to square yards.

6,300 \div 9 = 700\text{ sq yd}

There are 9 square feet in one square yard (

3\text{ ft} \times 3\text{ ft}

), and the turf is priced per square yard.

Calculate the total cost.

700 \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.

PreviousPage 2 / 2

Rectangular Area Applications

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes