Explanation:

- In a square, both diagonals are equal. So, we equate the given diagonal lengths: \(4k + 6 = 7k - 3\).

- Solve the equation:

\[ 4k + 6 = 7k - 3 \]

\[ 6 + 3 = 7k - 4k \]

\[ 9 = 3k \]

\[ k = 3 \]

- Substitute \(k = 3\) back into either diagonal equation:

\[ 4k + 6 = 4(3) + 6 = 18 \]

- The diagonal of the square is 18 cm.

- The formula for the diagonal (\(d\)) of a square with side \(a\) is \(d = a\sqrt{2}\).

- So, \(a\sqrt{2} = 18\); solve for \(a\):

\[ a = \frac{18}{\sqrt{2}} = 9\sqrt{2} \]

- Area of the square (\(a^2\)) is:

\[ (9\sqrt{2})^2 = 81 \times 2 = 162 \, \text{cm}^2 \]

- Option 2 is correct: 162 cm²