What is the area of square with an diagonal of `sqrt(2)`?

Options

A. `(1)/(2)`
B. `1`
C. `sqrt(2)`
D. `2`

Answer

To find the area of a square with a diagonal of \( \sqrt{2} \), we can follow these steps:

### Step 1: Understand the relationship between the side and diagonal of a square.
The diagonal \( d \) of a square is related to its side length \( a \) by the formula:
\[ d = a \sqrt{2} \]

### Step 2: Set up the equation using the given diagonal.
We are given that the diagonal \( d \) is \( \sqrt{2} \). Therefore, we can set up the equation:
\[ a \sqrt{2} = \sqrt{2} \]

### Step 3: Solve for the side length \( a \).
To find \( a \), we can divide both sides of the equation by \( \sqrt{2} \):
\[ a = \frac{\sqrt{2}}{\sqrt{2}} = 1 \]

### Step 4: Calculate the area of the square.
The area \( A \) of a square is given by the formula:
\[ A = a^2 \]
Substituting \( a = 1 \) into the area formula:
\[ A = 1^2 = 1 \]

### Conclusion:
The area of the square is \( 1 \).

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