The base of a triangular pyramid is a triangle with corners at #(7 ,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 · 2016-03-14T12:16:49

Volume #V=10" "#cubic units

Let #P_1(7, 7)#, and #P_2(5, 3)#,and # P_3(8, 4)#

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[(7,5,8,7),(7,3,4,7)]#

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

#A=1/2(21+20+56-35-24-28)#

#A=1/2(97-87)#

#A=5#

Volume #V=1/3*Ah=1/3*5*6=30/3=10#

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