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Difficulty: EasyPerimeter and Fencing Problems

A school is installing a new fence around a square play area. Each side of the play area measures 55 yards. If the fencing material costs $0.50\$0.50 per foot, what is the total cost of the fencing required?

  1. A
    $10.00\$10.00
  2. $30.00\$30.00Answer
  3. C
    $112.50\$112.50
  4. D
    $300.00\$300.00

Answer

$30.00\$30.00
The correct answer is found by first ensuring the units match. Since the cost is provided per foot, convert the 55-yard sides into feet (5×3=155 \times 3 = 15 feet). Next, find the perimeter of the square play area (15×4=6015 \times 4 = 60 feet). Finally, multiply the 6060-foot perimeter by the $0.50\$0.50 per foot cost to determine a total fencing cost of $30.00\$30.00.

Step-by-Step Solution

1
Convert the side length from yards to feet.
5 yards×3=15 feet5 \text{ yards} \times 3 = 15 \text{ feet}
The cost of fencing is given per foot, so all geometric measurements must be converted to feet before calculating the total cost.
2
Calculate the perimeter of the square play area.
4×15 feet=60 feet4 \times 15 \text{ feet} = 60 \text{ feet}
The fence goes around the outer boundary, which is the perimeter of the square.
3
Calculate the total cost by multiplying the perimeter by the cost per foot.
60 feet×$0.50/foot=$30.0060 \text{ feet} \times \$0.50/\text{foot} = \$30.00
To find the total cost, multiply the total linear feet of fencing needed by the given price per foot.

Key Concept

Calculating perimeter of a square and applying unit conversions to determine total cost.
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Topics

Perimeter and Fencing Problems

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