# The base of a triangular pyramid is a triangle with corners at #(2 ,5 )#, #(6 ,3 )#, and #(7 ,8 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?

##### 1 Answer

Nov 1, 2016

#### Explanation:

#A(2;5)" " B(6;3)" " C(7;8)#

#AB=2sqrt(5)#

The line passing through

#y-5=(3-5)/(6-2)*(x-2)#

that in implicit form gets

#x+2y-12=0#

The distance of

#h=|1*7+2*8-12|/sqrt(5)=(23-12)/sqrt(5)=11/sqrt(5)#

The base area is

#AB*h/2=2*sqrt(5)*11/(2*sqrt(5))=11#

The volume of pyramid is

#("base area " xx " heigth")/3=11*15/3=55#