In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k − 3)$ cm. The area of the square (in cm²) is:

Since the diagonals of a square are equal, we can set the two expressions for the diagonals equal to each other:

$4k + 6 = 7k - 3$

Now, solve for $k$:

$6 + 3 = 7k - 4k$

$9 = 3k$

$k = 3$

Now, substitute $k$ back into one of the diagonal expressions to find the length of the diagonal:

Diagonal = $4(3) + 6 = 12 + 6 = 18$ cm.

The area of the square can be calculated using the formula for the area in terms of the diagonal:

Area = $\frac{d^2}{2}$, where $d$ is the length of the diagonal.

Area = $\frac{18^2}{2} = \frac{324}{2} = 162$ cm².

Thus, the area of the square is 162 cm².