The surface of the pyramid is the surface of all its faces and its base.
We start with the base, that is a square base of side 4 cm.
Then the surface of the base is:
[tex]A_b=l^2=4^2=16\operatorname{cm}^2[/tex]
Now, we calculate the area of one of the faces.
The height of the triangle that forms the face is equal to the slant height of the pyramid, which is 8 cm in this case.
The base of the triangle is the side of the base, and its length is 4 cm.
Then, the surface of the face of the pyramid is:
[tex]A_f=\frac{b\cdot h}{2}=\frac{4\cdot8}{2}=\frac{32}{2}=16\operatorname{cm}^2[/tex]
The surface of the pyramid is equal to the the surface of the base and the 4 faces, which has the same area.
Then, we can calculate the surface of the pyramid as:
[tex]A_p=A_b+4A_f=16+4\cdot16=16+64=80\operatorname{cm}^2[/tex]
Answer: 80 cm^2
