If the wire in the shape of square of perimeter 44 cm is turned into a circle with same circumference, then find the area of the circle formed.

Options

A. `77 cm^(2)`
B. `308 cm^(2)`
C. `154 cm^(2)`
D. `231 cm^(2)`

Answer

To solve the problem step by step, we need to follow these instructions:

### Step 1: Find the length of the wire
The wire is shaped into a square with a perimeter of 44 cm. The perimeter of a square is given by the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]
Let the side of the square be \( s \). Therefore:
\[ 4s = 44 \]
Dividing both sides by 4 gives:
\[ s = \frac{44}{4} = 11 \text{ cm} \]

### Step 2: Find the circumference of the circle
Since the wire is turned into a circle with the same circumference as the perimeter of the square, the circumference \( C \) of the circle is also 44 cm.

### Step 3: Use the circumference to find the radius
The formula for the circumference of a circle is:
\[ C = 2\pi r \]
Substituting the circumference we have:
\[ 44 = 2\pi r \]
To find \( r \), we rearrange the equation:
\[ r = \frac{44}{2\pi} = \frac{22}{\pi} \]

### Step 4: Calculate the area of the circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi \left(\frac{22}{\pi}\right)^2 \]
Calculating \( r^2 \):
\[ r^2 = \frac{484}{\pi^2} \]
Now substituting back into the area formula:
\[ A = \pi \times \frac{484}{\pi^2} = \frac{484}{\pi} \]
Using \( \pi \approx \frac{22}{7} \) for calculation:
\[ A = \frac{484 \times 7}{22} = \frac{3388}{22} = 154 \text{ cm}^2 \]

### Final Answer
The area of the circle formed is \( 154 \text{ cm}^2 \).

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