The length of the diagonal of a square is `4 sqrt 2` cms. Its area is

Options

A. `32 cm^2`
B. `16 cm^2`
C. `8 cm^2`
D. `36 cm^2`

Answer

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

### Step 1: Understand 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:
\[ d = s\sqrt{2} \]

### Step 2: Substitute the given diagonal length into the formula.
We are given that the diagonal \( d = 4\sqrt{2} \) cm. Substituting this into the formula gives:
\[ 4\sqrt{2} = s\sqrt{2} \]

### Step 3: Solve for the side length \( s \).
To isolate \( s \), divide both sides of the equation by \( \sqrt{2} \):
\[ s = \frac{4\sqrt{2}}{\sqrt{2}} = 4 \text{ cm} \]

### Step 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 \( s \):
\[ A = 4^2 = 16 \text{ cm}^2 \]

### Final Answer:
The area of the square is \( 16 \text{ cm}^2 \).

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