The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(5 ,3 )#, and #(8 ,4 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

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Answer 1 · 2016-03-23T09:06:03

Volume #V=11" "#cubic units

Compute the area of the triangular base first

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

Area #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)#

The given points are #P_1(6, 7)#, #P_2(5, 3)#, #P_3(8, 4)#

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

Area #A=1/2[(6,5,8,6),(7,3,4,7)]#

Area #A=1/2*(6*3+5*4+8*7-5*7-8*3-6*4)#

Area #A=1/2*(18+20+56-35-24-24)#

Area #A=1/2*(94-83)#

Area #A=1/2*(11)=5.5#

Compute the volume of the triangular pyramid

#V=1/3*A*h=1/3*11/2*6#

#V=11" "#cubic units

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