The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(1 ,7 )#, and #(5 ,4 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

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Answer 1 · 2016-03-13T01:41:13

Volume #V=20/3" "#cubic units

Compute the area of the triangular base:

#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)#

Let
#P_1(6,2)#
#P_2(5, 4)#
#P_3(1,7)#

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

#A=1/2[6*4+5*7+1*2-5*2-1*4-6*7]#

#A=1/2(24+35+2-10-4-42)#

#A=1/2(61-56)#
#A=5/2#

Now compute the volume of the Pyramid

#V=1/3*A*h=1/3*5/2*8#

#V=20/3" "#cubic units

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