SOLUTION: Find the volume of a figure consisting of a pyramid with a right triangle base sitting atop a prism with the same right triangle base. The base and height of the triangle base are

Algebra ->  Equations -> SOLUTION: Find the volume of a figure consisting of a pyramid with a right triangle base sitting atop a prism with the same right triangle base. The base and height of the triangle base are       Log On


   

Question 973598: Find the volume of a figure consisting of a pyramid with a right triangle base sitting atop a prism with the same right triangle base. The base and height of the triangle base are 13yd and 20yd. The height of the prism is 9yd. The height from the bottom of the base of the prism to the tip of the pyramid is 27yd.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
In the drawing below, the two red dots are where the red 27 yd altitude of
the entire figure intersects the top and bottom of the prism base on which
the pyramid sits.  I have split the 27 yd altitude into 9 yd at the bottom
and 18 yd. at the top. 



We break the figure into two parts:

This prism with a right triangle base:



The area of the right triangle bottom (and top) 
is found by 

A%22%22=%22%22expr%281%2F2%29%2Abase%2Aheight%29%22%22=%22%22expr%281%2F2%29%2A13%2A20%22%22=%22%22130yd˛.

The volume of this prism is

V%22%22=%22%22%28Area_of_base%29%2Aheight%29%22%22=%22%22130%2A5%22%22=%22%22650ydł.

and sitting on top of that prism is this pyramid:


 
The volume of this pyramid is

V%22%22=%22%22expr%281%2F3%29%2Aarea_of_base%2Aheight%29%22%22=%22%22expr%281%2F3%29%2A130%2A18%22%22=%22%22780ydł.

We add the two volumes together:

Total volume = 650ydł + 780ydł = 1430ydł

Edwin