Question 973598
<pre>
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. 

{{{drawing(400,400,-6,7,-2,11, 
locate(2.5,1.5,20),locate(5.1,4.3,9),locate(-2,1,13),
red(
circle(1,2,0.15),circle(1,2,0.13),circle(1,2,0.11),circle(1,2,0.09),circle(1,2,0.07),circle(1,2,0.05),circle(1,2,0.03),circle(1,2,0.01),

circle(1,4,0.15),circle(1,4,0.13),circle(1,4,0.11),circle(1,4,0.09),circle(1,4,0.07),circle(1,4,0.05),circle(1,4,0.03),circle(1,4,0.01)),




line(-3,2,-3,4),
line(-3,4,1,9),
line(1,9,5,5),
line(5,5,5,3),
line(5,3,0,0),
line(0,0,-3,2),

line(0,0,0,2),
line(0,2,-3,4),
line(0,2,5,5),
line(1,9,0,2),

green(line(-3,4,5,5),line(-3,2,5,3)),red(line(1,2,1,9),locate(1.1,6.5,18),
locate(1.1,3.5,9)))}}}

We break the figure into two parts:

This prism with a right triangle base:

{{{drawing(400,400,-6,7,-2,11, 
locate(2.5,1.5,20),locate(5.1,4.3,9),locate(-2,1,13),



line(-3,2,-3,4),


line(5,5,5,3),
line(5,3,0,0),
line(0,0,-3,2),

line(0,0,0,2),
line(0,2,-3,4),
line(0,2,5,5),line(-3,4,5,5),


green(line(-3,2,5,3))

  )}}}

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

{{{A}}}{{{""=""}}}{{{expr(1/2)*base*height)}}}{{{""=""}}}{{{expr(1/2)*13*20}}}{{{""=""}}}{{{130}}}yd˛.

The volume of this prism is

{{{V}}}{{{""=""}}}{{{(Area_of_base)*height)}}}{{{""=""}}}{{{130*5}}}{{{""=""}}}{{{650}}}ydł.

and sitting on top of that prism is this pyramid:

{{{drawing(400,400,-6,7,-2,11, 
line(-3,4,1,9),
line(1,9,5,5),

red(
circle(1,4,0.15),circle(1,4,0.13),circle(1,4,0.11),circle(1,4,0.09),circle(1,4,0.07),circle(1,4,0.05),circle(1,4,0.03),circle(1,4,0.01)),



line(0,2,-3,4),
line(0,2,5,5),
line(1,9,0,2),

green(line(-3,4,5,5)),red(line(1,4,1,9),locate(1.1,6.5,18))

  )}}}
 
The volume of this pyramid is

{{{V}}}{{{""=""}}}{{{expr(1/3)*area_of_base*height)}}}{{{""=""}}}{{{expr(1/3)*130*18}}}{{{""=""}}}{{{780}}}ydł.

We add the two volumes together:

Total volume = 650ydł + 780ydł = 1430ydł

Edwin</pre>