# The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

##### 1 Answer

Mar 5, 2016

#### Explanation:

Area of base, a triangle

#S_(base)=(1/2)|[[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]]|#

#S_(base)=(1/2)|[[7,6,1],[4,1,1],[3,2,1]]| =(1/2)| [7+18+8-(3+14+24)] |=(1/2)|[33-41]|=(1/2) 8=4#

The volume of a pyramid is

So

#V=(4*7)/3=28/3 " cubic units"~=9.333 " cubic units"#