A square-shaped lawn has an area of 62,500 square meters. What is the cost of building a fence around it at a rate of $5.5 per meter?
Understand the Problem
The question is asking to calculate the cost of building a fence around a square-shaped lawn with a specified area. We need to first determine the perimeter based on the area and then multiply that by the given rate per meter for the cost.
Answer
The cost of building the fence is $5,500.
Answer for screen readers
The total cost of building the fence is $5,500.
Steps to Solve
- Calculate the side length of the lawn
To find the side length of a square given its area, use the formula:
$$ \text{Area} = \text{side}^2 $$
Rearranging the formula to solve for the side length gives:
$$ \text{side} = \sqrt{\text{Area}} = \sqrt{62500} $$
- Find the perimeter of the lawn
The perimeter ( P ) of a square is given by the formula:
$$ P = 4 \times \text{side} $$
Using the value found in the previous step, calculate the perimeter.
- Calculate the cost of the fence
To find the total cost of building the fence, multiply the perimeter ( P ) by the cost per meter:
$$ \text{Cost} = P \times \text{rate} $$
Using the perimeter calculated and the rate of $5.5 per meter, determine the total cost.
The total cost of building the fence is $5,500.
More Information
To construct a fence for a square lawn of area 62,500 square meters, we find that the cost will be influenced primarily by the perimeter, making this a practical application of both geometry and basic multiplication in budgeting.
Tips
- Incorrectly calculating the side: Forgetting to take the square root of the area or using the wrong area.
- Misunderstanding perimeter: Confusing perimeter with area, which can lead to incorrect calculations for the cost.
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