The only information given in the problem is the radius. From the radius, we are expected to solve for the perimeter. But in order to do so, we have to go through a few small steps. The initial goal is to solve for the length of one of the sides. Once one of the sides has been found, the perimeter can be solved for by multiplying the side length by the number of sides ($\displaystyle 6$). 

In order to solve for the side (or as some call it, the base side), we can use right triangles. 

The first step is to solve for the internal angles of the hexagon. This can be solved through $\displaystyle \frac{180(n-2)}{n}$, where $\displaystyle n$ is the number of sides. 

$\displaystyle \frac{180(6-2)}{6}$

$\displaystyle \frac{180(4)}{6}$ 

$\displaystyle 120^{\circ}$ = internal angle measurement 

This angle gets bisected in the right triangle we can draw using the radius. This means that the bottom right corner of the figure is $\displaystyle 60^{\circ}$. Now that we have one side and one angle measure, we can solve for the base of the triangle in one of two ways. 
1. Using trigonometric functions (SOH CAH TOA)
2. Remembering the rules of a 30/60/90 triangle

Using the rules of the 30/60/90 triangle, where the hypotenuse equals the $\displaystyle h$ value and the side opposite of $\displaystyle 30^{\circ}$ (in this case, our base) is $\displaystyle \frac{h}{2}$. Because $\displaystyle h=2$, this means that our base is $\displaystyle 1$; however, because the base of the triangle only makes up half of the length of a side, this means that the side length is actually $\displaystyle 2\:cm$. 

Now that we have the value of the side length, we can solve for the perimeter using the formula mentioned previously:

$\displaystyle P=2\cdot6=12$

$\displaystyle P=12\:cm$

The perimeter of a hexagon is:

$\displaystyle P=6s$

Substitute the side length and solve for the perimeter.

$\displaystyle P=6(6ab)=36ab$

Write the perimeter formula for a hexagon.  Substitute the side length and solve.

$\displaystyle P=6s=6(\sqrt6)=6\sqrt6$

A hexagon has 6 sides.  

Given the length of the side is 100, the perimeter is:

$\displaystyle P=6s = 6\cdot100 =600$

Write the formula for the perimeter of a hexagon.

$\displaystyle P=6s$

Substitute the side and simplify.

$\displaystyle P=6\left(\frac{a}{2}\right)=3a$

Write the perimeter formula for a hexagon, substitute the side length, and simplify.

Remember to distribute the 6 through to all parts within the parentheses.

$\displaystyle P=6s=6(a+2b) = 6a+12b$

Write the formula for the perimeter of a hexagon, substitute the length of the side, and simplify.

$\displaystyle P=6s=6\left(\frac{2}{3}abc\right)=4abc$

Write the formula for the perimeter of a hexagon.

$\displaystyle P=6s$

Since $\displaystyle 3a$ equals two sides of a hexagon, one side will have a length of $\displaystyle \frac{3a}{2}=1.5a$.

Substitute this length into the perimeter formula and evaluate.

$\displaystyle P=6s=6(1.5a)=9a$

Substitute the length $\displaystyle \frac{a}{6}+\frac{b}{24}$ into the hexagon perimeter formula and simplify.

Remember to distribute the 6 to all parts within the parentheses.

$\displaystyle P=6s = 6\left(\frac{a}{6}+\frac{b}{24}\right) = a+\frac{b}{4}$

When all the opposite sides of a regular hexagon are connected, you should notice that six congruent equilateral triangles are created:

Thus, the diagonal of the hexagon is twice the length of a side.

$\displaystyle \text{Diagonal}=2(\text{side})$

$\displaystyle \text{Side}=\frac{\text{Diagonal}}{2}$

Plug in the given diagonal to find the length of a side.

$\displaystyle \text{Side}=\frac{14}{2}=7$

Now, recall how to find the perimeter of a regular hexagon:

$\displaystyle \text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter.

$\displaystyle \text{Perimeter}=6(7)=42$