The base of a triangular pyramid is a triangle with corners at #(6 ,1 )#, #(2 ,4 )#, and #(4 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

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Answer 1 · 2017-01-25T14:53:30

#2/3 unit^3#

let say #x_1=6,x_2=2,x_3=4, y_1=1,y_2=4 and y_3=3#

pyramid volume #=1/3#base areaheight

Base area #=1/2|[(x_1*y_2)+(x_2*y_3)+(x_3*y_1)]-[(y_1*x_2) +(y_2*x_3)+(y_3*x_1)]|#

#=1/2|[(6*4)+(2*3)+(4*1)]-[(1*2)+(4*4)+(3*6)]|#

#=1/2|(24+6+4)-(2+16+18)|#

#=1/2|34-36|#
#=1/2*2=1 unit^2#

Therefore the pyramid's volume #=1/3*1*2=2/3 unit^3#