What is the volume of the square pyramid?

V = 621.4 mm^3

Step-by-step explanation:

The volume of this pyramid is V = (1/3)(base area)(height).  We must calculate the height from the info given.  Draw in a vertical line to represent the height.  Imagine a triangle with hypotenuse 12.8 mm (given) and shorter leg (13 mm)/2, or 6.5 mm.

The Pythagorean Theorem applies here:  h^2 + (6.5 mm)^2 = (12.8 mm)^2.  We get:  h^2 + 42.25 = 163.84, or h^2 = 121.59, or h = √121.59, or

h = 11.03 mm.

Then, as before, the volume of this prism is V = (1/3)(base area)(height), or with specific numerical values   V = (1/3)(13 mm)^2(11.03 m), or

V = 621.4 mm^3