The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,5 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

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Answer 1 · 2016-06-05T02:07:56

#V=8" "#cubic units

the volume #V# of a triangular pyramid has the formula

Volume = 1/3 of Area of base * Height of pyramid

Let us compute the area #A# of the base with
#P_1(x_1, y_1)=(6, 2)#
#P_2(x_2, y_2)=(3, 5)#
#P_3(x_3, y_3)=(4, 2)#

#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[(6, 3, 4, 6),(2, 5, 2, 2)]#

#A=1/2*[6*5+3*2+4*2-3*2-4*5-6*2]#

#A=1/[30+6+8-6-20-12]#

#A=1/2(44-38)#

#A=3" "#square units

Let us now compute the volume V of the pyramid

#V=1/3*A*h#

#V=1/3*3*8#

#V=8" "#cubic units

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