The base of a triangular pyramid is a triangle with corners at #(2 ,7 )#, #(5 ,3 )#, and #(8 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

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Answer 1 · 2018-03-26T08:12:49

#5.67# cubic units

First Of All, Find the Area of the Triangular Base.

So, The Area of the Base of The Pyramid :-

#1/2{x_1(y_2 -y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}#

[If The Coordiantes for the vertices of the triangles are #(x_1,y_1),#

#(x_2,y_2) and (x_3,y_3)# respectively.]

#= 1/2{2(3-2) + 5(2-7) + 8(7 - 3)}# sq. units

#= 1/2{2 -25 +40}# sq. units

#= 1/2(17)# sq. units

#= 8.5# sq. units.

So, The Volume of The Triangular Pyramid

#= 1/3(ah)# [Where #a# is the area of the base and #h# is the height of the pyramid.]

#= 1/3 (8.5*2)# cubic units

#= 17/3# cubic units

#=5.67# cubic units (approx.)

Hope this helps.