A square has a perimeter of $28 \text{ cm}.$ What is the area of the square, in $\mbox{cm}^2?$
Since the four sides of a square are equal in length and the perimeter is $28,$ then each side has length $\frac{28}{4}=7.$  The area of the square is the product of the length and width, which are each equal to $7.$ Therefore, the area of the square in $\mbox{cm}^2$ is $7\times7=\boxed{49}.$