The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,1 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

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Answer 1 · 2016-03-13T09:48:03

Volume #V=1/3*Ah=1/3*1*8=8/3=2 2/3#

Let #P_1(6, 2)#, and #P_2(4, 2)#,and # P_3(3, 1)#

Compute the area of the base of the pyramid
#A=1/2[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]#

#A=1/2[x_1y_2+x_2y_3+x_3y_1-x_2y_1-x_3y_2-x_1y_3]#

#A=1/2[(6,4,3,6),(2,2,1,2)]#

#A=1/2(6*2+4*1+3*2-2*4-2*3-1*6)#

#A=1/2(12+4+6-8-6-6)#

#A=1#

Volume #V=1/3*Ah=1/3*1*8=8/3=2 2/3#

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