How to Get the Perimeter of a Hexagon: A Simple Step-by-Step Guide

The perimeter of a hexagon is the total distance around its boundary. Calculating the perimeter is a straightforward process that requires knowledge of the hexagon's side length or apothem. In this article, we'll provide a simple step-by-step guide on how to get the perimeter of a hexagon, along with some essential formulas and examples to help you understand the concept better.

A hexagon is a polygon with six sides, and its perimeter is the sum of the lengths of all its sides. There are two types of hexagons: regular and irregular. A regular hexagon has all sides of equal length, while an irregular hexagon has sides of different lengths. The method for calculating the perimeter of a hexagon varies depending on the type of hexagon and the information available.

Understanding Hexagons

Before we dive into the calculation of the perimeter, let's take a brief look at the properties of hexagons. A hexagon is a polygon with six sides, and its internal angles add up to 720 degrees. The sum of the external angles of a hexagon is always 360 degrees.

Types of Hexagons

There are two main types of hexagons: regular and irregular.

• A regular hexagon has all sides of equal length and all internal angles equal to 120 degrees.
• An irregular hexagon has sides of different lengths and internal angles that vary.

Calculating the Perimeter of a Regular Hexagon

Calculating the perimeter of a regular hexagon is a simple process. Since all sides of a regular hexagon are equal, you can use the following formula:

Perimeter = 6 × side length

For example, if the side length of a regular hexagon is 5 cm, the perimeter would be:

Perimeter = 6 × 5 cm = 30 cm

Calculating the Perimeter of an Irregular Hexagon

Calculating the perimeter of an irregular hexagon is slightly more complex. Since the sides of an irregular hexagon have different lengths, you need to add up the lengths of all its sides:

Perimeter = side1 + side2 + side3 + side4 + side5 + side6

For example, if the side lengths of an irregular hexagon are 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, and 8 cm, the perimeter would be:

Perimeter = 3 cm + 4 cm + 5 cm + 6 cm + 7 cm + 8 cm = 33 cm

Using the Apothem to Calculate the Perimeter

In some cases, you may be given the apothem of a hexagon instead of the side length. The apothem is the distance from the center of the hexagon to one of its vertices. For a regular hexagon, you can use the apothem to calculate the side length and then the perimeter:

Side length = apothem × 2 / √3

Once you have the side length, you can calculate the perimeter using the formula:

Perimeter = 6 × side length

Example

If the apothem of a regular hexagon is 4 cm, you can calculate the side length as follows:

Side length = 4 cm × 2 / √3 ≈ 4.62 cm

Then, the perimeter would be:

Perimeter = 6 × 4.62 cm ≈ 27.72 cm

Real-World Applications

Calculating the perimeter of a hexagon has numerous real-world applications. For example, architects use the perimeter of hexagons to design buildings, bridges, and other structures. Engineers use the perimeter to calculate the stress and strain on hexagonal-shaped components. Designers use the perimeter to create visually appealing patterns and shapes.

Conclusion

In conclusion, calculating the perimeter of a hexagon is a straightforward process that requires knowledge of the hexagon's side length or apothem. By understanding the properties of hexagons and using the formulas provided, you can easily calculate the perimeter of regular and irregular hexagons. The applications of hexagon perimeter calculations are vast, and this concept is essential for professionals in various fields.