A wire is in a circular shape of radius 28 cm. If it is bent in the form of a square, what will bethe area of the square formed? 

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Find the Length of the Wire
The length of the wire is equal to the circumference of the circle. The formula for the circumference \( C \) of a circle is given by:

\[ C = 2\pi r \]

Where \( r \) is the radius of the circle. Given that the radius \( r = 28 \) cm, we can substitute this value into the formula.

\[ C = 2 \times \pi \times 28 \]

Using \( \pi \approx \frac{22}{7} \):

\[ C = 2 \times \frac{22}{7} \times 28 \]

Calculating this gives:

\[ C = 2 \times 22 \times 4 = 176 \text{ cm} \]

### Step 2: Relate the Length of the Wire to the Perimeter of the Square
When the wire is bent into the shape of a square, the length of the wire will equal the perimeter of the square. The formula for the perimeter \( P \) of a square is:

\[ P = 4 \times \text{side} \]

Let \( s \) be the length of one side of the square. Thus, we have:

\[ 176 = 4s \]

### Step 3: Solve for the Side Length of the Square
To find the side length \( s \), we can rearrange the equation:

\[ s = \frac{176}{4} \]

Calculating this gives:

\[ s = 44 \text{ cm} \]

### Step 4: Calculate the Area of the Square
The area \( A \) of a square is given by:

\[ A = s \times s \]

Substituting the value of \( s \):

\[ A = 44 \times 44 \]

Calculating this gives:

\[ A = 1936 \text{ cm}^2 \]

### Final Answer
The area of the square formed is \( 1936 \text{ cm}^2 \).

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