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Difficulty: MediumRectangular Area Applications

A city planner is designing a rectangular public square that measures 60 yards60 \text{ yards} by 40 yards40 \text{ yards}. The entire square will be paved with brick, except for a central rectangular fountain that measures 10 yards10 \text{ yards} by 8 yards8 \text{ yards}. If the paving bricks cost $2.50\$2.50 per square foot, what is the total cost of the bricks needed for the square in dollars?

Answer: 52200

Answer

52200
The correct answer is 52200becausethenetareaofthesquaretobepavedis52200 because the net area of the square to be paved is 2,320 squareyards( square yards ( 2400 \text{ sq yd total} - 80 \text{ sq yd fountain}).Since). Since 1 squareyardequals square yard equals 9 squarefeet,thisconvertsto square feet, this converts to 20,880 squarefeet.Multiplyingthetotalsquarefootagebythebrickcostof square feet. Multiplying the total square footage by the brick cost of \2.502.50 per square foot yields a total cost of $52,200\$52,200.

Step-by-Step Solution

1
Calculate the total area of the public square in square yards.
2400 sq yd2400 \text{ sq yd}
The total area is the product of its length and width (60 yards×40 yards60 \text{ yards} \times 40 \text{ yards}).
2
Calculate the area of the central fountain in square yards.
80 sq yd80 \text{ sq yd}
The area of the fountain is the product of its length and width (10 yards×8 yards10 \text{ yards} \times 8 \text{ yards}).
3
Subtract the fountain's area from the total area to find the net paved area in square yards.
2320 sq yd2320 \text{ sq yd}
The fountain will not be paved, so its area must be removed from the total square yardage (2400−802400 - 80).
4
Convert the net area from square yards to square feet.
20880 sq ft20880 \text{ sq ft}
The cost of the bricks is given per square foot. Since 1 yard=3 feet1 \text{ yard} = 3 \text{ feet}, 1 square yard=3×3=9 square feet1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}. Therefore, we multiply the area in square yards by 99 (2320×9=208802320 \times 9 = 20880).
5
Calculate the total cost by multiplying the net area in square feet by the price per square foot.
5220052200
Multiplying the total square footage (2088020880) by the cost per square foot ($2.50\$2.50) yields the final cost in dollars.

Key Concept

Subtractive area calculations and square unit conversions
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Topics

Rectangular Area Applications

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