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:
![A_b=l^2=4^2=16\operatorname{cm}^2]()
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:
![A_f=(b\cdot h)/(2)=(4\cdot8)/(2)=(32)/(2)=16\operatorname{cm}^2]()
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:
![A_p=A_b+4A_f=16+4\cdot16=16+64=80\operatorname{cm}^2]()
Answer: 80 cm^2