Question

The base of a triangular pyramid is a triangle with corners at `(9 ,5 )`, `(6 ,5 )`, and `(7 ,8 )`. If the pyramid has a height of `15`, what is the pyramid's volume?

Answer 1

Volume of pyramid `22.5` cubic unit

Explanation:

Volume of a pyramid is 1/3.base area.hight. Base area is the area of triangle ABC of sides `AB=sqrt((9-6)^2+(5-5)^2)=3 ; BC =sqrt((6-7)^2+(5-8)^2)=sqrt 10=3.16 ; CA=sqrt((7-9)^2+(8-5)^2)=sqrt13=3.61` Semi perimeter of the triangle `s=1/2(3+3.1+3.61) =4.885` Area `=sqrt(4.885*(4.885-3)(4.885-3.16)(4.885-3.61)) = 4.5` sq units Hence volume of pyramid `=1/3*4.5*15 =22.5` cubic unit [Ans]