Volume of a prism from a pentagonal prism

volume of a prism = area of base * height

Here is a top-down view of the base.

As you can see, it can be split into 5 triangles.

The area of each triangle = (1/2)(2)(4 tan 36º)(4) = 16 tan 36º

So...

the area of the base = 5 * 16 tan 36º = 80 tan 36º

And so..

the volume of the prism = 80 tan 36º * 16 = 1,280 tan 36º ≈ 929.974 cubic cm

The radius of the pentagon can be found as :

4/sin 54°

And the area of the base  =

5 (1/2) [4/sin(54°)]^2 * sin(72°) =  40 sin (72°) /[sin(54°)]^2

So.....the volume is

Base * Height  =

 40 sin (72°) /[sin(54°)]^2 *  16   ≈  929.97 cubic cenimeters = 930 cubic centimeters