Hexagon – Definition, Types, Properties, Examples, FAQs
Geometry is an essential part of basic math that every kid will encounter from grade to grade. At first, kids get acquainted with simple basic shapes like circles, triangles, rectangles, squares, and the like. However, as time passes, they encounter more complicated shapes like hexagons. If you teach kids about the hexagon, you must learn a few things about it. This article contains all the information you need to know about the hexagon.
What is a Hexagon?
A hexagon is a 6 sided polygon which can also be described as a closed 6 sided shape where all the sides are straight and equal, as well as the angles. While you may not see hexagons every day and everywhere, they exist in some real-life objects’ forms which you may come across occasionally.
You can find the hexagon shape in honeycombs and stop signs. In some cases, the hexagons come in the middle of other things, and you may have to look twice to see them; for example, soccer balls, floor tiles, and nuts and bolts. If your kid asks, “What does a hexagon look like?”, you can search for the items attached to the hexagon definition to get a physical representation of the shape.
Types of hexagon
The types of hexagon are differentiated according to their sides and angles. There are two significant hexagons, regular and irregular, and others. Here are some of the hexagons in the world of geometry:
A regular hexagon is a hexagon where all 6 sides are of the same length and all angles are equal to 120 degrees, with the sum of all interior angles being 720 degrees. The sum of the exterior angles for any polygon is 360 degrees, so each exterior angle of the regular hexagon is 60 degrees. You would find such hexagons everywhere, in the stop sign, soccer balls, and honeycombs.
An irregular hexagon is the one where all the sides and angles are unequal. Unlike a regular hexagon where all the sides and angles are equal, an irregular hexagon can have angles of different sizes and sides of different lengths. You can find irregular hexagons in objects like rocks or buildings with designs that you will describe as asymmetrical. However, irregular hexagons are not seen in many everyday objects, so if you need to show a visual representation of an irregular hexagon to a child, you might need to search harder.
Some types of hexagons are not usually discussed in early mathematics because kids do not have to use them until they advance in their grades. These types of hexagons are as follows:
- Concave hexagon
- Convex hexagon
- Symmetrical hexagon
- Asymmetrical hexagon
You do not need to worry about these hexagons for now as kids will not be learning them.
Classification of hexagons based on their angles
You can classify hexagons according to the size of their interior angles, and here are these categories:
An acute hexagon is the one in which all 6 internal angles are less than 90 degrees. You can find acute hexagon angles in snowflakes and architectural designs of some buildings.
In an obtuse hexagon, all 6 internal angles are greater than 90 degrees but lesser than 180 degrees. Because of their irregular shapes, you will not find obtuse hexagons in many places. But some people use them as patterns in artworks.
In a right hexagon, all of the six angles are just equal to 90 degrees. So, another name for right-angle hexagons is rectangular or 90-degree hexagons. You can find the right hexagons in tile designs, artwork, and architecture.
Properties of hexagons
Before you can solve a problem involving a hexagon, you must first know the properties of a hexagon, and here are some of them:
- A hexagon has 6 sides and 6 angles.
- A hexagon has 6 vertices where all the sides meet.
- The sum of the interior of a hexagon is always equal to 720 degrees.
- In a regular hexagon, the 6 interior angles measure and are equal to 120 degrees. This sum can change with irregular angles.
- The size of the exterior angles is always 60 degrees.
- A regular hexagon has six lines of symmetry which you can use to divide the hexagon into 6 congruent parts.
- The hexagon’s perimeter is the sum of the length of the six sides.
- The area of a hexagon is 3√3s2/2, where s is the length of one side.
- A hexagon has 9 diagonals, defined as line segments connecting nonadjacent vertices.
The hexagon sides are 6 in number. In a regular hexagon, all the sides are of equal length, while in an irregular hexagon, some of the sides, at least two, will be of different lengths. The sum of all of the hexagon’s sides is the hexagon’s perimeter. If you know the length of one of the sides and the perimeter of a regular hexagon, you can get the length of the rest by dividing the perimeter by 6. Note that this formula above may not work if you are dealing with irregular hexagons.
Hexagon angles are 6 in number. In a regular hexagon, all 6 angles are equal to 120. You can calculate each angle by dividing the total sum of all the angles by six (720÷6). The process is a little different if you are dealing with an irregular hexagon. You have to divide the hexagon into triangles and then calculate the angle of each triangle, which naturally should be 180 degrees. Alternatively, you can use (n-2)x180 degrees, with n representing the number of sides; this is the sum of interior angles for any polygon. At the end of the calculation, regardless of the angles’ measures, the sum must be 720 degrees.
Perimeter of a hexagon
The perimeter of a hexagon is the total length of all 6 sides of the hexagon. If you know the length of one side of a regular hexagon, you can calculate the perimeter using p=6s, with s being one side of the hexagon and p being the perimeter. In an irregular hexagon, you will need to add up each side to get the sum which would now be the perimeter.
Area of a hexagon
The formula to calculate the area of a regular hexagon is A = (3√3 / 2) × s². A is the area of a hexagon, and s is the length of the hexagon’s sides.
Alternatively, you can use the formula A = (3√3 / 2) × a² if you have something called the apothem. The apothem is the distance from the center of the hexagon to the midpoint of one of its sides.
In this formula, A stands for the apothem of length.
You can only use these two formulas if you are working with a regular hexagon; if you are calculating the area for an irregular hexagon, you must break the hexagon into smaller shapes and calculate their areas individually.
Solved examples on hexagon
Here are some solved examples on a hexagon that would help you understand better how the formulas work:
Example 1: Find the perimeter of a regular hexagon with a side length of 6 cm.
A regular hexagon has six equal sides, so you get the perimeter of the hexagon by multiplying 6 by the length of one of its sides.
Perimeter of hexagon = 6 x side length
= 6 x 6 cm
= 36 cm
Therefore, the perimeter of the regular hexagon is 36 cm.
Example 2: Find the area of a regular hexagon with an apothem length of 8 cm.
The formula for finding the area of a regular hexagon is:
Area of hexagon = 3 x √3 x (apothem length)² ÷ 2
Given, apothem length = 8 cm
Area of hexagon = 3 x √3 x (8 cm)² ÷ 2
= 3 x √3 x 64 cm² ÷ 2
= 96√3 cm²
Therefore, the area of the regular hexagon is 96√3 cm².
Example 3:The distance between two opposite vertices of a regular hexagon is 12 cm. Find its side length.
S is the side length of the regular hexagon.
A regular hexagon’s distance between two opposite vertices equals twice the apothem length.
Therefore, 2a = 12 cm, where a is the apothem length.
Dividing both sides by 2, we get:
a = 6 cm
The apothem length can also be calculated using the formula a = s√3/2, where s is the side length.
Substituting a = 6 cm and solving for s, we get:
6 = s√3/2
s = 12/√3 cm
Therefore, the side length of the regular hexagon is 12/√3 cm (or approximately 6.93 cm).
What are the angles of a hexagon?
The angles of a hexagon are 6 angles, 120 degrees each for regular hexagons and different measures for irregular angles, but all must get a sum of 720 degrees.
How many sides does a hexagon have?
A hexagon has 6 sides.
How many types of hexagons are there?
There are two significant types of hexagons, regular and irregular hexagons.
What is the sum of all interior angles of a hexagon?
The sum of all interior angles of a hexagon is 720 degrees.
How many diagonals does a hexagon have?
A hexagon has 9 diagonals.
Does a hexagon always have equal sides?
Regular hexagons have equal sides; irregular hexagons may have different sides’ lengths.
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