The base of a triangular pyramid is a triangle with corners at #(7 ,5 )#, #(6 ,9 )#, and #(3 ,4 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?

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Answer 1 · 2016-09-10T14:40:36

Area of a triangle given three vertices #(x_1, y_1)# , #(x_2,y_2)#, #(x_3,y_3)# is:

#A = abs((x_1(y_2-y_3) + x_2(y_3-y_1) +x_3(y_1-y_2))/2#

#(x_1,y_1) =(7,5)#
#(x_2,y_2)=(6,9)#
#(x_3,y_3) =(3,4)#

#A=abs((7(9-4)+6(4-5)+3(5-9))/2#

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

#A=abs((-35-6-12)/2#

#A=abs(-53/2) =26.5#

Volume of a trianglar pyramid = #V= 1/3Ah# where A is the area of the triangular base and h is the height of the pyramid.

#V=1/3*26.5*15 = 132.5#