The area of a square field is 484 `m^(2)`. Find :
the length of its diagonal, correct to two places of decimal.

Answer

To find the length of the diagonal of a square field when the area is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between area and side length of a square**:
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
where \( s \) is the length of one side of the square.

2. **Given the area**:
We know that the area \( A \) of the square field is \( 484 \, m^2 \).

3. **Find the side length**:
To find the side length \( s \), we can rearrange the area formula:
\[ s = \sqrt{A} \]
Substituting the given area:
\[ s = \sqrt{484} \]
Calculating the square root:
\[ s = 22 \, m \]

4. **Use the formula for the diagonal of a square**:
The length of the diagonal \( d \) of a square can be calculated using the formula:
\[ d = s\sqrt{2} \]
Substituting the value of \( s \):
\[ d = 22\sqrt{2} \]

5. **Calculate the diagonal**:
To find the value of \( \sqrt{2} \), we can use the approximation \( \sqrt{2} \approx 1.414 \):
\[ d \approx 22 \times 1.414 \]
Performing the multiplication:
\[ d \approx 31.11 \, m \]

6. **Final answer**:
Therefore, the length of the diagonal of the square field is approximately:
\[ d \approx 31.11 \, m \]