A pyramid has a square base, whose side is 8 cm. If the height of pyramid is 16 cm, then what is the total surface area (in cm$$^2$$) of the pyramid?

Area of the base of Pyramid is = $$\left(8\times8\right)\ cm=\ 64\ cm.$$

Curved or lateral surface area of pyramid

=1/2×(perimeter of base)×slant height

Slant height = $$\sqrt{16^2+\left(\frac{8}{2}\right)^2}=\sqrt{256+16}=\sqrt{272}=4\sqrt{17}.$$

So, Curved surface area = $$\frac{1}{2}\times32\times4\sqrt{17}=64\sqrt{17}.$$

So, Total surface area= $$64\sqrt{17}+64=64\left(\sqrt{17}+1\right)\ cm^2.$$

A is correct choice.