Question

find the area of a regular hexagon with an apothem 3.5 miles long and a side length of 4 miles

Answer 1

You actually don't need the apothem here unless you want to do this method:

Double the apothem = W = the distance from one flat side to the other (think like the diameter of a circle)
\[Area = \frac{\sqrt{3}}{2}W^2\]

Answer 2

\[ Area = \frac{3\sqrt{3}}{2}\cdot (side)^2 \]

Answer 3

I would use the second formula, and it agrees with other sources I've checked.