Hello, shilo!
i have a right hexagonal prism,
and i need to find the SA and the volume for it.
what formula do i use? I assume your exam will not include such a sloppy question . . .
Code:
* - *
* A *
| * - * |
| | | |
| | | | h
| | | |
| | | |
* | | *
* - *
We know nothing about the hexagon.
We must be given its perimeter $\displaystyle P$, and its area $\displaystyle A.$
. . (or be given enough information so we can find $\displaystyle P$ and $\displaystyle A$.)
The height $\displaystyle h$ is perpendicular to the two hexagonal bases.
The surface area consists of the top and bottom: .$\displaystyle 2A$
. . and the lateral area: .$\displaystyle Ph$
Therefore, the total surface area is: .$\displaystyle \boxed{ SA \:=\:2A + Ph}$
The volume is (area of base) × (height): .$\displaystyle \boxed{V \:=\:Ah}$