Question

The base of a triangular pyramid is a triangle with corners at `(7 ,8 )`, `(2 ,3 )`, and `(8 ,3 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

Volume of pyramid is `30.0` cubic unit

Explanation:

Triangle's sides are
`A=sqrt((7-2)^2+(8-3)^2) =sqrt50=7.07`
`B=sqrt((2-8)^2+(3-3)^2) =sqrt36=6.0`
`A=sqrt((8-7)^2+(3-8)^2) =sqrt26=5.1:.`Semi perimeter:`s=(A+B+C)/2=9.09:.` Base area: `A_b = sqrt(s(s-a)(s-b)s-c))=sqrt(9.09(9.09-7.07)(9.09-6)(9.09-5.1))=15.0:.`Volume of pyramid: `v=1/3*A_b*ht =1/3*6*15=30.0` cubic unit[Ans]