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 $1/3xx0.496xx4=0.661$

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