The base of a pentagonal prism is regular with an apothem of 6 centimeters. The height of the prism is 10 centimeters. Find the volume of the prism. Round your answer to the nearest cubic centimeter.
Create a triangle on the pentagon using the apothem, a radius, and one-half of a side.
The angle between the radius and the side is: 54o. (540o / 5 / 2)
This makes the one-half side: tan(54) = 6/s ---> s = 4.359
So the area of that triangle is: ½ x 4.359 x 6 = 13.08
There are 1o triangle of this size, so the area of the pentagon is 130.8
Volume = 130.8 x 10 = 1308 cu cm.