Find the area of a square, the length of whose diagonal is `8sqrt2` m.

Options

A. 7 m
B. 8 m
C. 9 m
D. 6 m

Answer

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

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

### Step 2: Substitute the given diagonal length into the formula.
Given that the diagonal \(d = 8\sqrt{2}\) m, we can substitute this value into the formula:
\[ 8\sqrt{2} = a\sqrt{2} \]

### Step 3: Solve for the side length \(a\).
To find \(a\), we can divide both sides of the equation by \(\sqrt{2}\):
\[ a = \frac{8\sqrt{2}}{\sqrt{2}} = 8 \text{ m} \]

### Step 4: Calculate the area of the square.
The area \(A\) of a square is given by the formula:
\[ A = a^2 \]
Substituting the value of \(a\):
\[ A = 8^2 = 64 \text{ m}^2 \]

### Final Answer:
The area of the square is \(64 \text{ m}^2\).

---