Question

The base of a triangular pyramid is a triangle with corners at `(6 ,7 )`, `(4 ,5 )`, and `(8 ,4 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

`10` [cubic units]

Explanation:

Area of the pyramid's base

`S_(base)=(1/2)|[[6,7,1],[4,5,1],[8,4,1]]|`
`S_(base)=(1/2)|30+56+16-(40+28+24)|=(1/2)|102-92|=5`

Volume of the pyramid
:`V=(S_(base)*height)/3`
`V=(5*6)/3=10` [cubic units]