We know that the area of the square is the square of the side length.
We also know that the perimeter is 4 times the side length.
So if we know the area, we have to find the side length and then calculate the perimeter.
If A is the area and x is the side length, we have:
![\begin{gathered} A=x^2 \\ 4\operatorname{cm}^2=x^2 \\ x=\sqrt[]{4\operatorname{cm}^2} \\ x=2\operatorname{cm} \end{gathered}]()
We now know the side length (x=2 cm).
Then, we can calculate the perimeter P as:
![P=4x=4\cdot2\operatorname{cm}=8\operatorname{cm}]()
Answer: the perimeter of a 4cm²-area square is 8 cm
If the perimeter is 108 cm, we can calculate the side length and then the area as:
![\begin{gathered} P=4x=108\operatorname{cm} \\ x=\frac{108\operatorname{cm}}{4} \\ x=27\operatorname{cm} \end{gathered}]()
![A=x^2=(27\operatorname{cm})^2=729\operatorname{cm}^2]()
Answer: when the perimeter of a square is 108 cm, its area is 729 cm^2