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Zorluk: Çok zorRectangular Area Applications

A contractor is installing new flooring in a rectangular hall that measures 24 feet24\text{ feet} by 36 feet36\text{ feet}. Inside the hall, there is a rectangular stage measuring 12 feet12\text{ feet} by 9 feet9\text{ feet} that will not receive new flooring. The flooring material is sold in boxes that each cover 2 square yards2\text{ square yards} and cost $45.50\$45.50 per box. Assuming no waste, what is the total cost of the boxes needed to complete the job?

  1. A
    $591.50\$591.50
  2. $1,911.00\$1,911.00Cevap
  3. C
    $3,822.00\$3,822.00
  4. D
    $5,733.00\$5,733.00

Cevap

$1,911.00\$1,911.00
The correct answer is found by calculating the net surface area and converting the units properly. The hall's area is 864 square feet and the stage's area is 108 square feet, leaving a net area of 756 square feet. Because 1 square yard equals 9 square feet, this converts to 84 square yards. Dividing by 2 square yards per box gives 42 boxes. At 45.50each,thetotalcostis45.50 each, the total cost is 1,911.00.

Adım Adım Çözüm

1
Calculate the total area of the hall in square feet.
24×36=864 sq ft24 \times 36 = 864\text{ sq ft}
To find the maximum possible flooring area before accounting for the unfloored stage.
2
Calculate the area of the stage in square feet.
12×9=108 sq ft12 \times 9 = 108\text{ sq ft}
The stage will not receive new flooring, so its area must be determined for subtraction.
3
Calculate the net area to be floored.
864−108=756 sq ft864 - 108 = 756\text{ sq ft}
Subtracting the stage area from the hall area gives the actual surface area that requires new flooring.
4
Convert the net area from square feet to square yards.
756÷9=84 sq yd756 \div 9 = 84\text{ sq yd}
The flooring boxes measure coverage in square yards. There are 9 sq ft9\text{ sq ft} in 1 sq yd1\text{ sq yd} (3 ft×3 ft3\text{ ft} \times 3\text{ ft}).
5
Determine the number of boxes needed.
84÷2=42 boxes84 \div 2 = 42\text{ boxes}
Each box covers 2 sq yd2\text{ sq yd}, so dividing the total square yards by the coverage per box yields the required number of boxes.
6
Calculate the total cost of the boxes.
42×$45.50=$1,911.0042 \times \$45.50 = \$1,911.00
Multiplying the total number of boxes by the price per box gives the final project cost.

Anahtar Kavram

Calculating net rectangular area with cutouts, converting between square units, and applying rates to find total material cost.
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Rectangular Area Applications

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