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

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Answer 1 · 2017-06-24T08:25:55

The volume of the pyramid is #=4/3u^3#

The area of the base triangle is

#A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|#

#A=1/2|(3,4,1),(2,7,1),(3,6,1)|#

#=1/2(3*|(7,1),(6,1)|-4*|(2,1),(3,1)|+1*|(2,7),(3,6)|)#

#=1/2(3(7-6)-4(2-3)+1(12-21))#

#=1/2(3+4-9)#

#=1/2|-2|=1#

The height is #h=4#

The volume of the pyramid is

#V=1/3*A*h#

#=1/3*1*4=4/3#