The circumference of circular field is 14 m then find out the area?

Answer

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

### Step 1: Understand the relationship between circumference and radius
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given circumference
We are given that the circumference of the circular field is 14 m. Therefore, we can set up the equation:
\[ 2\pi r = 14 \]

### Step 3: Solve for the radius \( r \)
To find the radius, we can rearrange the equation:
\[ r = \frac{14}{2\pi} = \frac{7}{\pi} \]

### Step 4: Use the radius to find the area
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Now, substitute the value of \( r \):
\[ A = \pi \left(\frac{7}{\pi}\right)^2 \]

### Step 5: Simplify the area expression
Calculating \( r^2 \):
\[ \left(\frac{7}{\pi}\right)^2 = \frac{49}{\pi^2} \]
Thus, substituting back into the area formula:
\[ A = \pi \cdot \frac{49}{\pi^2} = \frac{49}{\pi} \]

### Step 6: Approximate the area using \( \pi \approx \frac{22}{7} \)
To get a numerical value, we can substitute \( \pi \) with \( \frac{22}{7} \):
\[ A \approx \frac{49}{\frac{22}{7}} = 49 \cdot \frac{7}{22} = \frac{343}{22} \]

### Final Answer
The area of the circular field is:
\[ \frac{343}{22} \text{ m}^2 \]

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