+0  
 
0
29
1
avatar

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.

 May 18, 2020
 #1
avatar+20883 
0

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.

 May 18, 2020

15 Online Users

avatar