The base of a triangular pyramid is a triangle with corners at #(5 ,8 )#, #(3 ,4 )#, and #(4 ,8 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

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Answer 1 · 2016-11-21T05:28:48

#V=4" "#cubic units

To solve for the volume of the pyramid which is
#V=1/3*area*height#

Solve for the area of the triangle first with #P_1(3, 4),P_2(5, 8),P_3(4, 8)#

the area A matrix

#A=1/2*[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]#

#A=1/2*(x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3)#

#A=1/2*[(3,5,4,3),(4,8,8,4)]#

#A=1/2*[3(8)+5(8)+4(4)-5(4)-4(8)-3(8)]#

#A=1/2*(24+40+16-20-32-24)#

#A=1/2*(80-76)#

#A=2#

Now the volume V

#V=1/3*area*height#

#V=1/3*2*6=4#

#V=4" "#cubic units

God bless....I hope the explanation is useful.