The circumference of a circle is 264 cm. Find its area. 

Answer

To find the area of a circle given its circumference, we can follow these steps:

### Step 1: Write down the formula for the circumference of a 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.

### Step 2: Substitute the given circumference into the formula.
We know that the circumference \( C \) is 264 cm. So we can write:
\[ 2 \pi r = 264 \]

### Step 3: Solve for the radius \( r \).
We can rearrange the formula to find \( r \):
\[ r = \frac{C}{2 \pi} \]
Substituting the value of \( C \):
\[ r = \frac{264}{2 \pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{264}{2 \times \frac{22}{7}} = \frac{264 \times 7}{2 \times 22} \]
Calculating the denominator:
\[ 2 \times 22 = 44 \]
So we have:
\[ r = \frac{264 \times 7}{44} \]
Now simplifying \( \frac{264}{44} \):
\[ \frac{264}{44} = 6 \]
Thus:
\[ r = 6 \times 7 = 42 \text{ cm} \]

### Step 4: Calculate the area of the circle.
The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Substituting \( r = 42 \) and \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (42)^2 \]
Calculating \( (42)^2 \):
\[ (42)^2 = 1764 \]
Now substituting back into the area formula:
\[ A = \frac{22}{7} \times 1764 \]
Calculating \( \frac{1764}{7} \):
\[ \frac{1764}{7} = 252 \]
Now substituting this value:
\[ A = 22 \times 252 \]
Calculating \( 22 \times 252 \):
\[ A = 5544 \text{ cm}^2 \]

### Final Answer:
The area of the circle is \( 5544 \text{ cm}^2 \).

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