The diagonal of a square is 3.2 m. Its area is:

Options

A. `10.24m^2`
B. `2.56m^2`
C. `3.41m^2`
D. `5.12m^2`

Answer

To find the area of a square when 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 its side length \( a \) by the formula:
\[ d = a\sqrt{2} \]
where \( d \) is the length of the diagonal.

2. **Substitute the given diagonal length**:
We know the diagonal \( d = 3.2 \) m. Therefore, we can write:
\[ 3.2 = a\sqrt{2} \]

3. **Solve for the side length \( a \)**:
To find \( a \), rearrange the equation:
\[ a = \frac{3.2}{\sqrt{2}} \]
To simplify this, multiply the numerator and the denominator by \( \sqrt{2} \):
\[ a = \frac{3.2 \sqrt{2}}{2} \]
\[ a = 1.6\sqrt{2} \]

4. **Calculate the area of the square**:
The area \( A \) of a square is given by:
\[ A = a^2 \]
Substitute \( a = 1.6\sqrt{2} \):
\[ A = (1.6\sqrt{2})^2 \]
\[ A = 1.6^2 \cdot (\sqrt{2})^2 \]
\[ A = 2.56 \cdot 2 \]
\[ A = 5.12 \text{ m}^2 \]

5. **Final Answer**:
The area of the square is:
\[ \boxed{5.12 \text{ m}^2} \]