The base of a pentagonal prism is regular with an apothem of 4 centimeters. The height of the prism is 16 centimeters. Find the volume of the prism. Round your answer to the nearest cubic centimeter

Guest Apr 6, 2017

#1**+3 **

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

hectictar
Apr 6, 2017