What is Hexagon? Definition, Types with Examples

hexagon is a common shape we usually see around us in floor tiles, beehives, and even in some nuts and bolts. But what is a hexagon and how many sides does a hexagon have? A hexagon is a two-dimensional (2D) closed shape. It is a polygon with six sides, six corners (called vertices), and six inside angles. To discover more about the definition of hexagon, its properties, types and examples, keep reading.

Read More:  Triangle

What is a Hexagon?

In geometry, the definition of hexagon states that it is a flat 2D closed shape that has six sides and six corners. The word “hexa” means six, and “gon” means angles, so a hexagon is a shape with six angles. There are two main types of hexagons.

• A regular hexagon has all six sides of the same length and all six angles equal.

• An irregular hexagon has sides and angles that can be different from each other.

Some common examples of hexagon shapes are honeycombs made by bees, the shape of a pencil’s end, and snowflakes. The total of all the inside angles of any hexagon is always 720 degrees.

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Examples of Hexagon Shapes in Real Life

Hexagons are shapes that appear both in nature and in things made by people. They are useful because of their strong and space-saving design. Here are some common examples of hexagon shapes we see in real life:

• Honeycombs: Bees make honeycombs using many small cells shaped like hexagons. This shape helps bees save wax and fit the most honey in a small space.

• Snowflakes: When water freezes, many snowflakes form six-sided shapes called hexagons. This gives snowflakes their beautiful and unique patterns.

• Basalt Columns: Some types of rocks, like basalt, cool down and crack into hexagon shapes. These natural columns can be seen in popular places like the Giant’s Causeway.

• Quartz Crystals: Minerals such as quartz grow inside the Earth in shapes that look like hexagons.

• Hexagon Tiles: People use tiles shaped like hexagons to cover floors and walls because these tiles fit together perfectly without leaving empty spaces.

• Architecture: Hexagons are used in the design of many famous buildings because they are strong and look interesting. Some well-known buildings with hexagon shapes include the New York Supreme Court Building, the Museum of Jewish History in Manhattan, and Berlin-Tegel Airport.

• Maps: Hexagons are also very useful in map-making. When showing things like population or land shapes on maps, hexagons fit together perfectly without leaving empty spaces. This helps maps show details more clearly and accurately, especially on curved surfaces like the Earth.

Read More: Area of a Circle

Key Properties of Hexagon

As we've learned by now, a hexagon is a flat, two-dimensional shape with six sides. It can have sides and angles that are all equal, or they can be different depending on the type of hexagon. Here are some important properties of hexagon that help us understand it better:

Sides and Vertices of Hexagon Shape

• A hexagon has 6 sides, 6 edges, and 6 vertices, or corners, where the sides meet.

• In a regular hexagon, all the sides are equal in length.

• The opposite sides of a regular hexagon are parallel to each other.

Interior and Exterior Angles

• The sum of all interior angles in any hexagon is always 720 degrees.

• In a regular hexagon, each interior angle measures 120 degrees.

• Each exterior angle of a regular hexagon measures 60 degrees, and all exterior angles together add up to 360 degrees.

Diagonals and Shape Type

• A hexagon has 9 diagonals. These are line segments connecting non-adjacent corners.

• A regular hexagon is a convex shape because all its interior angles are less than 180 degrees.

Symmetry and Equal Parts

• A regular hexagon is symmetrical and has 6 lines of symmetry.

• It can be divided into 6 equal equilateral triangles.

It is important for students to keep a note of these properties of a hexagon, as they help in understanding the shape better and solving related math problems easily.

Read More: Symmetry - Types, Facts and Examples

Types of Hexagon in Math

As we know, hexagons are six-sided shapes, but they have different properties. Based on their sides and angles, hexagons can be grouped into different types. Let’s understand the main types of hexagon shapes one by one:

1. Regular Hexagon

A regular hexagon is a shape that has six sides, and all the sides are of the same length. Not only the sides, but all the angles inside this hexagon are also equal.

• Each interior angle measures exactly 120 degrees.

• A regular hexagon also has six lines of symmetry, which means it looks the same if we fold or rotate it in different ways.

• Because of this balance in shape and angles, regular hexagons are often seen in nature and designs. One common example of a regular hexagon is the honeycomb made by bees.

2. Irregular Hexagon

An irregular hexagon also has six sides, but the sides and angles are not all equal. Some sides may be longer, and some may be shorter.

• The angles can also vary, but the total of all the interior angles is always 720 degrees.

• Unlike regular hexagons, irregular hexagons do not have equal symmetry and may look uneven.

• These are often found in art and decoration, such as randomly shaped tiles used in patterns.

3. Convex Hexagon

In a convex hexagon, all the corners point outward, and each interior angle is less than 180 degrees. A convex hexagon can be either regular or irregular.

• This means it may have equal sides and angles or different ones, but none of its sides bend inward.

• Convex hexagons usually have a neat, outward-looking shape, and many symmetrical designs are based on this type.

• A good example of a convex hexagon is a neatly cut hexagonal gemstone.

4. Concave Hexagon

A concave hexagon is a six-sided shape where at least one corner bends inward. Because of this inward dip, the shape looks like it has a dent or fold.

• Concave hexagon has at least one of its interior angles greater than 180 degrees.

• Concave hexagons do not usually have symmetry and look quite different from the regular ones.

• A star-shaped figure with an inward point is an example of a concave hexagon.

5. Complex Hexagon

A complex hexagon is not easy to recognize at first glance. It may have very uneven sides and angles or may even have lines that cross over each other. Some complex hexagons can also be self-intersecting, which means their sides overlap or twist.

• The interior angles in such hexagons can vary a lot, and symmetry is either limited or not present at all.

• One example of this is a star-shaped hexagon with crossing lines in the middle.

Read More: What are Whole Numbers?

Area of Hexagon

To find the area of a hexagon, we usually use a formula. But this only works when the hexagon is regular, which means all six sides are equal in length, and all angles are the same.

The formula to find the area of a regular hexagon is: Area = (3√3 / 2) × a².

Here, a is the length of one side of the hexagon. This formula helps us find how much space the hexagon covers on a flat surface.

Read More: Formula To Find Midpoint

Perimeter of Hexagon

The perimeter of a hexagon means the total distance around the outer edge of the hexagon. To find the perimeter, we simply add the lengths of all six sides.

• If the hexagon is regular (all sides are equal), we can use a simple formula: Perimeter = 6 × a. Here, a = length of one side.

• But if the hexagon is irregular (sides are not equal), then we need to add all six sides one by one: Perimeter = a + b + c + d + e + f. Where a, b, c, d, e, and f are the lengths of each side.

Finding the perimeter helps us know how long the border of the shape is. This is useful in solving mathematical questions based on fencing a garden or designing hexagon-shaped floor tiles.

Practice Questions Based on Hexagon Geometry Formulas

Q.1. Find the perimeter of a regular hexagon if each side is 9 cm long.

Solution: Perimeter = 6 × side
= 6 × 9 = 54 cm.

Q.2. The perimeter of a regular hexagon is 72 cm. What is the length of one side?

Solution: Perimeter = 6 × side
72 = 6 × side
Side = 72 ÷ 6 = 12 cm

Q.3. Five angles of a hexagon are 100° each. Find the measure of the sixth angle.

Solution: Sum of all interior angles = 720°
Sum of five angles = 5 × 100 = 500°
Sixth angle = 720 – 500 = 220°

Q.4. Find the area of a regular hexagon with side length 4 cm.

Solution: Area = (3√3 / 2) × side²
= (3√3 / 2) × 4²
= (3√3 / 2) × 16
= 24√3
≈ 41.57 cm²

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