find the area of a regular hexagon with the given measurement.

2 sqrt3 apothem

a =

There are 6 sides to a hexagon. 360/6 = 60. So each angle going out to each side measures 60 degrees. We can split one side in half to create a right triangle which has a 30 degree angle. The adjacent is the apothem. We want to find the opposite of this triangle because it will give us half the length of the side of the hexagon. So we can use tangent.





We know that :



Multiply  to both sides:



Simplify:



So half the side length of the hexagon is 2. That means the entire side length is 2 * 2 = 4.

Now use the formula:



This is used to calculate the area of any regular polygon. Where 'a' is the apothem and 'p' is the perimeter. The side length is 4, a hexagon has 6 sides, so the perimeter is 6 * 4 = 24. Plug in what we know:



Simplify:

The second and fourth answer are correct