Each diagonal of a square is 12 cm long. Its area is

Options

A. `144cm^(2)`
B. `72cm^(2)`
C. `36cm^(2)`
D. none of these

Answer

To find the area of a square when each diagonal is given, 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 know that the diagonal \(d\) is 12 cm. Therefore, we can set up the equation:
\[ 12 = s\sqrt{2} \]

### Step 3: Solve for the side length \(s\).
To find \(s\), we can rearrange the equation:
\[ s = \frac{12}{\sqrt{2}} \]
To simplify this, we can multiply the numerator and the denominator by \(\sqrt{2}\):
\[ s = \frac{12\sqrt{2}}{2} = 6\sqrt{2} \text{ cm} \]

### 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 \(s\):
\[ A = (6\sqrt{2})^2 = 36 \times 2 = 72 \text{ cm}^2 \]

### Final Answer:
The area of the square is \(72 \text{ cm}^2\).

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