The circumference of a circular field is 308 m. Find its :
area

Answer

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

### Step-by-Step Solution:

1. **Identify the formula for circumference**:
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

2. **Set up the equation with the given circumference**:
We know the circumference is 308 m, so we can set up the equation:
\[ 2 \pi r = 308 \]

3. **Substitute the value of \( \pi \)**:
We can use the approximation \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ 2 \times \frac{22}{7} \times r = 308 \]

4. **Solve for \( r \)**:
Rearranging the equation to solve for \( r \):
\[ r = \frac{308 \times 7}{2 \times 22} \]
Simplifying this:
\[ r = \frac{308 \times 7}{44} \]
\[ r = \frac{2156}{44} \]
\[ r = 49 \text{ m} \]

5. **Find the area using the radius**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting \( r = 49 \) m and \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (49)^2 \]

6. **Calculate \( (49)^2 \)**:
\[ (49)^2 = 2401 \]
Now substituting this back into the area formula:
\[ A = \frac{22}{7} \times 2401 \]

7. **Multiply and simplify**:
\[ A = \frac{22 \times 2401}{7} \]
Dividing \( 2401 \) by \( 7 \):
\[ 2401 \div 7 = 343 \]
Now, substituting this back:
\[ A = 22 \times 343 = 7546 \text{ m}^2 \]

### Final Answer:
The area of the circular field is \( 7546 \text{ m}^2 \).