Answer: The perimeter is [tex]a[/tex]
Step-by-step explanation:
1. By definition, the formula for calculate the surface area of a cube is:
[tex]SA=6s^{2}[/tex]
Where s is the lenght of any edge of the cube.
2. You know that the surface area of the cube of the problem is [tex]6(a/4)^{2}[/tex], therefore the lenght of each edge of the cube is:
[tex]s=a/4[/tex]
3. Each face of the cube is a square, therefore the perimeter of one face is:
[tex]P=4s[/tex]
[tex]P=4(a/4)[/tex]
[tex]P=4a/4[/tex]
[tex]P=a[/tex]
