The diagonal of a square is 'a' cm, then area of square is:

Options

A. 2a `cm^2`
B. `a/sqrt2cm^2`
C. `a^2/2cm^2`
D. `a^2/4cm^2`

Answer

To find the area of a square when the diagonal is given as 'a' cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the diagonal and the side of a square**:
The diagonal (d) of a square is related to its side length (s) by the formula:
\[ d = s \sqrt{2} \]
Here, we know that the diagonal is 'a' cm.

2. **Express the side in terms of the diagonal**:
Rearranging the formula to find the side length:
\[ s = \frac{d}{\sqrt{2}} = \frac{a}{\sqrt{2}} \text{ cm} \]

3. **Calculate the area of the square**:
The area (A) of a square is given by the formula:
\[ A = s^2 \]
Substituting the expression for the side:
\[ A = \left(\frac{a}{\sqrt{2}}\right)^2 \]

4. **Simplify the expression**:
\[ A = \frac{a^2}{2} \text{ cm}^2 \]

### Final Answer:
Thus, the area of the square is:
\[ \frac{a^2}{2} \text{ cm}^2 \]