Question

The base of a triangular pyramid is a triangle with corners at `(6 ,5 )`, `(7 ,1 )`, and `(4 ,7 )`. If the pyramid has a height of `7`, what is the pyramid's volume?

Answer 1

Volume of the pyramid is `6.95` cubic unit

Explanation:

The sides of triangular base `A=sqrt((6-7)^2+(5-1)^2)=sqrt17=4.12`;
`B=sqrt((7-4)^2+(1-7)^2)=sqrt45=6.71`;
`C=sqrt((4-6)^2+(7-5)^2)=sqrt8=2.83`; Semi perimeer `s=(4.12+6.71+2.83)/2=6.83`
Area of triangular base`A_t=sqrt(6.83*(6.83-4.12)(6.83-6.71)(6.83-2.83))=2.98`
Volume of the pyramid is `V=(1/3)*A_t*ht = (2.98*7)/3=6.95` cubic unit[Ans}