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?
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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#
