Find the volume of a regular hexagonal prism with the height of 22 apothem of 16 and a side length of 8

8778 cubic units
8558 cubic units
8448 cubic units
8668 cubic units

Step-by-step explanation:

The volume of a prism is given by:

where is the area of the base, and  is the height of thr prism.

We know that the height is:

u

and the bases of this prism are hexagons.

Thus the area of the base is the area of a regular hexagon:

where is the number of sides: for an hexagon:

is the length of each side: u,

and is the apothem:

we substitute all of this to find the area of the base:

and finally we use the formula for the volume:

we get the following:

which is the third option