If the diagonal of a square is 10 cm, then what is the area (in `cm^2` ) of the square?

Options

A. A. `50 sqrt2`
B. B. `50`
C. C. `25 sqrt2`
D. D. `25`

Answer

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

### Step-by-Step Solution:

1. **Understand the Relationship Between the Diagonal and the Side of the Square**:
The diagonal \( d \) of a square is related to its side length \( s \) by the formula:
\[ d = s\sqrt{2} \]

2. **Given the Diagonal**:
We know from the problem that the diagonal \( d \) is 10 cm.

3. **Calculate the Side Length**:
To find the side length \( s \), we can rearrange the formula:
\[ s = \frac{d}{\sqrt{2}} = \frac{10}{\sqrt{2}} = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \text{ cm} \]

4. **Calculate the Area of the Square**:
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
Substituting the value of \( s \):
\[ A = (5\sqrt{2})^2 = 25 \times 2 = 50 \text{ cm}^2 \]

5. **Final Answer**:
Therefore, the area of the square is \( 50 \text{ cm}^2 \).