The base of a triangular pyramid is a triangle with corners at #(3 ,5 )#, #(4 ,2 )#, and #(2 ,6 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

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Answer 1 · 2017-06-29T09:50:54

The volume is #=2.33u^3#

The area of the base triangle is calculated with the determinant

Therefore, the area of the base is

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

#A=1/2|(3,5,1),(4,2,1),(2,6,1)|#

#=1/2(3*|(2,1),(6,1)|-5*|(4,1),(2,1)|+1*|(4,2),(2,6)|)#

#=1/2(3(2-6)-5(4-2)+1(24-4))#

#=1/2(-12-10+20)#

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

The volume of the pyramid is

#=1/3*h*A=1/3*7*1=7/3=2.33u^3#