The length of the diagonal of a square is 24 cm. Find its area .

Answer

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

### Step-by-Step Solution:

1. **Identify the relationship between the diagonal and the side of the square**:
The diagonal \(d\) of a square is related to the side length \(s\) by the formula:
\[ d = s\sqrt{2} \]
Given that the diagonal \(d = 24 \, \text{cm}\), we can set up the equation:
\[ 24 = s\sqrt{2} \]

2. **Solve for the side length \(s\)**:
To find \(s\), we can rearrange the equation:
\[ s = \frac{24}{\sqrt{2}} \]
To simplify this, we can multiply the numerator and denominator by \(\sqrt{2}\):
\[ s = \frac{24\sqrt{2}}{2} = 12\sqrt{2} \, \text{cm} \]

3. **Calculate the area \(A\) of the square**:
The area \(A\) of a square is given by the formula:
\[ A = s^2 \]
Substituting \(s = 12\sqrt{2}\):
\[ A = (12\sqrt{2})^2 = 144 \times 2 = 288 \, \text{cm}^2 \]

4. **Final Answer**:
The area of the square is:
\[ A = 288 \, \text{cm}^2 \]