In the square pyramid shown below, the diagonal length fc = 16√2 centimeters and the height of the pyramid is 7 centimeters. find the slant height ad of the pyramid, to the nearest tenth. show your work with reasoning for each step.

Consider it under a triangle, 
So, Slant height will be hypotenuse, and height will be perpendicular & base.

We know,base diagonal = √2 * base
So, 16√2 = √2 * b
b = 16

Now, substitute it into the expression:
h² = 7² + 16²
h² = 49 + 256
h = √305
h = 17.5   [ To nearest tenth ]

In short, Your Answer would be: 17.5 cm

Hope this helps!