A square park has area `4356 m^2` . Taking its one round is same as taking one round of another circular park. Find the area of the circular park.

Options

A. `11088m^2`
B. `5544 m^2`
C. `22176m^2`
D. `1386m^2`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the side of the square park
Given the area of the square park is \( 4356 \, m^2 \).

The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]
Let the side of the square be \( a \). Therefore,
\[ a^2 = 4356 \]
To find \( a \), we take the square root of both sides:
\[ a = \sqrt{4356} \]
Calculating the square root:
\[ a = 66 \, m \]

### Step 2: Calculate the perimeter of the square park
The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
Substituting the value of the side:
\[ P = 4 \times 66 = 264 \, m \]

### Step 3: Set the perimeter of the circular park equal to the perimeter of the square park
The perimeter (circumference) \( C \) of a circular park is given by:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circular park. Since the perimeters are equal:
\[ 2\pi r = 264 \]

### Step 4: Solve for the radius \( r \)
Rearranging the equation to solve for \( r \):
\[ r = \frac{264}{2\pi} \]
Substituting \( \pi \approx \frac{22}{7} \):
\[ r = \frac{264}{2 \times \frac{22}{7}} = \frac{264 \times 7}{44} = \frac{1848}{44} = 42 \, m \]

### Step 5: Calculate the area of the circular park
The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (42)^2 \]
Calculating \( (42)^2 \):
\[ (42)^2 = 1764 \]
Now substituting back:
\[ A = \frac{22}{7} \times 1764 \]
Calculating the area:
\[ A = \frac{22 \times 1764}{7} = 22 \times 252 = 5544 \, m^2 \]

### Final Answer
The area of the circular park is \( 5544 \, m^2 \).

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