All ACT Math Resources
Example Question #33 : Plane Geometry
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?
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:
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 #34 : Plane Geometry
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 .
Example Question #35 : Plane Geometry
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:
Example Question #36 : Plane Geometry
The side length of a hexagon is . What is the perimeter?
Write the formula for the perimeter of a hexagon.
Substitute the given length.