If the length of diagonal BD of a square ABCD is 4.8 cm, the area of the square ABCD is :

Options

A. `9.6 cm^(2) `
B. `11.52 cm^(2) `
C. `12.52 cm^(2) `
D. `5.76 cm^(2)`

Answer

To find the area of square ABCD given the length of diagonal BD, follow these steps:

### Step 1: Understand the relationship between the diagonal and the sides of the square.
In a square, the diagonal can be calculated using the formula:
\[ d = a\sqrt{2} \]
where \(d\) is the length of the diagonal and \(a\) is the length of a side of the square.

### Step 2: Substitute the given value of the diagonal.
We know that the length of diagonal BD is 4.8 cm. Therefore, we can write:
\[ 4.8 = a\sqrt{2} \]

### Step 3: Solve for the side length \(a\).
To find \(a\), we rearrange the equation:
\[ a = \frac{4.8}{\sqrt{2}} \]
To simplify this, we can multiply the numerator and denominator by \(\sqrt{2}\):
\[ a = \frac{4.8\sqrt{2}}{2} = 2.4\sqrt{2} \]

### Step 4: Calculate the area of the square.
The area \(A\) of the square is given by:
\[ A = a^2 \]
Substituting the value of \(a\):
\[ A = (2.4\sqrt{2})^2 \]
Calculating this gives:
\[ A = 2.4^2 \cdot 2 = 5.76 \cdot 2 = 11.52 \text{ cm}^2 \]

### Final Answer:
The area of square ABCD is \(11.52 \text{ cm}^2\).

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