Question

The base of a triangular pyramid is a triangle with corners at `(5 ,8 )`, `(2 ,3 )`, and `(9 ,4 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

V=197.63

Explanation:

So Base values are given. Lets find the length of base:
1) length between (9,4) and (2,3)= `sqrt((3-4)^2+(2-9)^2)`
= `sqrt(50)=5sqrt2=7.07`
2)another side length between : (9,4) and (5,8)= `sqrt((4-8)^2+(9-5)^2)=4sqrt2=5.65`
3) side length between (2,3) and (5,8)= `sqrt((2-5)^2+(3-8)^2)=sqrt34=5.83`
Volume= `V=1/3*Area*h=1/3*4*Area`
To find Area, we should use Heron's formula : `p=(a+b+c)/2=9.275`
area= `sqrt[p^3*(p-a)*(p-b)*(p-c)]=148.2257`
`V=1/3*4*148.2257=197.63`