How to find the perimeter of a hexagon - ACT Math
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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?
The figure above is a regular hexagon.
What is the perimeter of the figure above?
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 
.
You can redraw the figure given to notice the little equilateral triangle that is formed within the hexagon. Since a hexagon can have the
Now, the
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
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What is the perimeter of a regular hexagon with an area of 
?
What is the perimeter of a regular hexagon with an area of
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 
.
The area of a regular hexagon is defined by the equation:
This is derived from the fact that the regular hexagon can be split up into
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
This means that
Therefore, the perimeter of the figure is equal to
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Find the perimeter of a hexagon with a side length of 
.
Find the perimeter of a hexagon with a side length of
There are 6 sides in a hexagon.
Therefore, given a side length of 16, the perimeter is:
There are 6 sides in a hexagon.
Therefore, given a side length of 16, the perimeter is:
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The side length of a hexagon is 
. What is the perimeter?
The side length of a hexagon is
Write the formula for the perimeter of a hexagon.
Substitute the given length.
Write the formula for the perimeter of a hexagon.
Substitute the given length.
Compare your answer with the correct one above