# ACT Math : How to find the perimeter of a hexagon

## Example Questions

### Example Question #1 : Hexagons

The figure above is a regular hexagon.  is the center of the figure. The line drawn is perpendicular to the side.

What is the perimeter of the figure above?

Explanation:

You can redraw the figure given to notice the little equilateral triangle that is formed within the hexagon. Since a hexagon can have the  degrees of its internal rotation divided up evenly, the central angle is  degrees. The two angles formed with the sides also are  degrees. Thus, you could draw:

Now, the  is located on the side that is the same as  on your standard  triangle. The base of the little triangle formed here is  on the standard triangle. Let's call our unknown value .

We know, then, that:

Or,

Now, this is only half of the size of the hexagon's side. Therefore, the full side length is .

Since this is a regular hexagon, all of the sides are of equal length.  This means that your total perimeter is  or .

### Example Question #2 : Hexagons

What is the perimeter of a regular hexagon with an area of ?

Explanation:

The area of a regular hexagon is defined by the equation:

, where  is the length of a side.

This is derived from the fact that the regular hexagon can be split up into  little equilateral triangles, each having an area of

To visualize this, consider the drawing:

Each triangle formed like this will be equilateral.  It is easiest to remember this relationship and memorize the general area equation for equilateral triangles. (It is useful in many venues!)

So, for your data, you know:

Solving for , you get:

This means that

Therefore, the perimeter of the figure is equal to  or .

### Example Question #3 : Hexagons

Find the perimeter of a hexagon with a side length of .

Explanation:

There are 6 sides in a hexagon.

Therefore, given a side length of 16, the perimeter is:

### Example Question #4 : Hexagons

The side length of a hexagon is .  What is the perimeter?