How to Find the Perimeter of a Hexagon

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  • 0:04 Steps to Solve
  • 1:29 Solution
  • 2:02 Tessellations and Application
  • 4:16 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

This lesson explains how to find the perimeter of a regular and an irregular hexagon. Once we know the process, we'll look at some examples of this shape in nature and an application of finding a hexagon's perimeter in our own lives.

Steps to Solve

A hexagon is a six-sided polygon. There are two types of hexagons, and those are regular hexagons and irregular hexagons. A regular hexagon is a hexagon in which all of its sides are equal in length. An irregular hexagon is a hexagon that is not regular; in other words, it's a hexagon with sides that are not all equal in length. A hexagon really is a beautiful shape, don't you agree?


perhex1


Now, let's talk about the perimeter of a hexagon. The perimeter of a hexagon is the distance around the hexagon. The process we use to find the perimeter of a hexagon is different for regular and irregular hexagons. Therefore, to find the perimeter of a hexagon, we first need to determine if it's regular or irregular.

If a hexagon is an irregular hexagon, we follow these steps to find the perimeter:

  1. Find the lengths of each of the sides of the hexagon.
  2. Add up all the lengths of the sides. This is your perimeter.

That's pretty straightforward. Thankfully, so is finding the perimeter of a regular hexagon. When a hexagon is a regular hexagon, we use the following steps to find its perimeter:

  1. Find the length of one of the sides of the hexagon.
  2. Multiply the length of one side of the hexagon by six. This is the perimeter of the hexagon.

That's pretty straightforward too, isn't it? In the case of a regular or irregular hexagon, finding the perimeter of a hexagon is a very simple process.

Solution

Let's go over that again. To find the perimeter of a hexagon, we first determine if the hexagon is regular or irregular, and then we proceed based on which one it is.

If a hexagon is irregular, we follow these steps:

  1. Find the lengths of each of the sides of the hexagon.
  2. Add up all the lengths of the sides. This is your perimeter.

If a hexagon is regular, we follow these steps:

  1. Find the length of one of the sides of the hexagon.
  2. Multiply the length of one of the sides of the hexagon by six. This is the perimeter of the hexagon.

Tessellations and Application

As we said before, hexagons are a beautiful shape. Not only that, but they show up extremely often in nature! For example, snowflakes often have hexagonal shapes in them.


perhex2


Another interesting nature example of a hexagon, and perhaps the most well-known example, is the honeycomb. Beehives are made up of rows of honeycombs that are made up of hexagonal cells in which the bees store pollen, honey, and eggs.


Honeycomb
perhex3


Notice that in a honeycomb, the hexagons share sides and produce a tiling of an area. Now, things get even more interesting. This tiling is an example of a tessellation. A tessellation is a pattern (or tiling) made up of shapes. The shapes fit together without any gaps, and they don't overlap, just like we observe in the honeycomb.

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