How does one measure the volume of a hexagonal cell? For example, a container with one closed end and hexagonal sides measuring four feet wide,(space between any two plane sides of said hexagon) and five feet in depth. How much liquid could a container of this size hold?

Do you mean a prism with a hexagonal cross section?

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Yes

Knowing the side length, the area of any regular polygon can be found by using

\text{Area}=\frac{L^{2}n}{4tan(\frac{\pi}{n})}

n=number of sides
L=side length

If you use a calculator make sure it is in radian mode.

For degree mode use \frac{L^{2}n}{4tan(\frac{180}{n})}

To find volume, multiply your result by the height of the container. In this case, 5.

This will be in cubic feet. To convert it to, say, gallons, multiply by 7.48