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 = 2d2, where d is the length of the diagonal.
Area = 2182=2324=162 cm².
Thus, the area of the square is 162 cm².