The base of a triangular pyramid is a triangle with corners at #(3 ,9 )#, #(1 ,6 )#, and #(2 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

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Answer 1 · 2016-03-18T12:48:19

Volume of pyramid is #0.661# units.

First to find area of base, let us find all the sides of base triangle.

#a=sqrt((1-3)^2+(6-9)^2)=sqrt(4+9)=sqrt13=3.606#

#b=sqrt((2-3)^2+(8-9)^2)=sqrt(1+1)=sqrt2=1.414#

#c=sqrt((2-1)^2+(8-6)^2)=sqrt(1+4)=sqrt5=2.236#

Now for using Heron's formula, #s=1/2(3.606+1.414+2.236)=7.256/2=3.628#

Hence, area of base triangle is

#sqrt(3.628xx(3.628-3.606)xx(3.628-1.414)xx(3.628-2.236)#

= #sqrt(3.628xx0.022xx2.214xx1.392)=0.496#

Hence, Volume of pyramid is #1/3xx0.496xx4=0.661#