Are you a fan of geometry or just someone who likes odd trivia? Either way, have you ever wondered what a 9 sided polygon is called? Believe it or not, it’s not a shape that we commonly encounter in our daily lives, but it does exist and it has a pretty unique name.
To be technical, a 9 sided polygon is called a nonagon. It’s what happens when you take a regular nine-sided shape with straight sides and connect all the points with straight lines to form a closed figure. While it might not be as common as a square or a circle, a nonagon pops up surprisingly often in math and geometry problems.
If you’re looking for fun facts about the nonagon, you’ll find that it has a few different unique properties. For instance, you can use it to create interesting patterns, as its symmetry makes it ideal for tessellations and creating repeating shapes. Additionally, it’s one of the shapes that can be used to create a magic star shape, where all the sides and internal angles add up to the same number!
Names of Different Polygon Shapes
Polygons are geometric shapes that have straight sides and angles. The term Polygon is derived from Greek words “poly,” which means many, and “gonia,” which means angles. The number of angles and sides a polygon has determines its name. In this article, we will be discussing the names of different polygon shapes.
Here are some of the most common polygon shapes along with their names, number of sides and angles:
- Triangle – 3 sides and 3 angles
- Quadrilateral – 4 sides and 4 angles
- Pentagon – 5 sides and 5 angles
- Hexagon – 6 sides and 6 angles
- Heptagon – 7 sides and 7 angles
- Octagon – 8 sides and 8 angles
- Nonagon – 9 sides and 9 angles
- Decagon – 10 sides and 10 angles
- Dodecagon – 12 sides and 12 angles
As shown above, polygons are named based on the number of sides and angles they possess. For instance, a six-sided polygon is called a Hexagon because of the six angles and sides it has. Similarly, a seven-sided polygon is called a Heptagon.
To further understand the different polygon shapes, here is a table that will help you visualize and distinguish between different polygons:
| Polygon Name | Number of Sides | Number of Angles |
|---|---|---|
| Triangle | 3 | 3 |
| Quadrilateral | 4 | 4 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 6 |
| Heptagon | 7 | 7 |
| Octagon | 8 | 8 |
| Nonagon | 9 | 9 |
| Decagon | 10 | 10 |
| Dodecagon | 12 | 12 |
Now that we have discussed the names of different polygon shapes and how they are named, you may encounter these shapes in your day-to-day activities. Knowing the names of these shapes can help you better understand mathematical concepts and everyday situations where polygons are used.
Properties of 9-Sided Polygons
A polygon is a closed planar figure bounded by straight line segments. A polygon with nine sides is called a Nonagon. A Nonagon is a type of convex polygon that has nine sides and nine angles. Like all polygons, a nonagon has properties that are unique to its shape and size.
Nine Properties of 9-Sided Polygons
- Each angle of a nonagon measures approximately 140 degrees.
- The interior angles of a nonagon add up to 1260 degrees.
- A nonagon can be inscribed in a circle.
- A regular nonagon is a type of polygon that has equal sides and angles.
- The distance around the outer edge of a nonagon is called its perimeter.
- The area of a nonagon can be calculated using the formula 9/2 x S² x Cot(180/9).
- The diagonals of a nonagon are the line segments that connect any two non-adjacent vertices.
- There are 54 diagonals in a nonagon.
- A nonagon is a type of polygon that can tessellate, meaning it can be arranged in a repeating pattern without any gaps or overlaps.
Types of Nonagons
There are many types of nonagons, including regular and irregular nonagons. A regular nonagon has nine sides of equal length and nine angles of equal measure. An irregular nonagon does not have sides or angles that are all the same length or measure. Some other types of nonagons include:
- Enneagram: A nonagon with two intersecting lines drawn from opposite vertices, forming an inner six-pointed star.
- Vesica Piscis: Two nonagons sharing the same center, but with the vertices of one residing on the sides of the other.
- Star Nonagon: A nonagon with lines drawn connecting every other vertex, resulting in a star-shaped figure.
Application of Nonagons
Nonagons can be seen in various aspects of life and art. The shape of a nonagon can be found in the design of some musical instruments such as a violin or a mandolin. It can also be seen in the structure of many buildings such as the U.S. Department of Energy Building in Washington D.C. Additionally, the nonagon has been used in many logos and symbols, including the symbol for the Enneagram, which is used in personality typing.
| Type of Nonagon | Properties |
|---|---|
| Regular Nonagon | 9 sides of equal length, 9 angles of equal measure |
| Irregular Nonagon | Sides and angles not all the same |
| Enneagram | 2 intersecting lines from opposite vertices, inner 6-pointed star |
| Vesica Piscis | Two nonagons sharing the same center point, with the vertices of one residing on the sides of the other |
| Star Nonagon | Lines drawn connecting every other vertex, resulting in a star-shaped figure |
Understanding the properties of 9-sided polygons can be useful in solving geometric problems and creating art and designs. The nonagon is a unique and interesting shape that can be found in various aspects of life.
Calculation of Interior and Exterior Angles of 9-Sided Polygons
A 9-sided polygon is called a nonagon. It is a plane figure with nine straight sides and nine angles. Calculating the interior and exterior angles of a nonagon requires some basic knowledge in geometry.
Before we delve into the specific calculations, let us first define the concepts of interior and exterior angles. Interior angles are those angles formed inside a polygon while exterior angles are those formed outside a polygon.
To calculate the interior angles of a nonagon, we can use the formula:
- Interior angle sum of a polygon = (n-2) x 180 degrees
- For a nonagon, n = 9, therefore:
- Interior angle sum of a nonagon = (9-2) x 180 degrees = 1260 degrees
- To find the measure of each interior angle of a nonagon, we can divide the sum by the number of angles, which is 9:
- Measure of each interior angle of a nonagon = 1260 degrees/9 = 140 degrees
On the other hand, to calculate the exterior angles of a nonagon, we can use the formula:
- Exterior angle of a polygon = 360 degrees/n
- For a nonagon, n = 9, therefore:
- Exterior angle of a nonagon = 360 degrees/9 = 40 degrees
To summarize, the interior angle of a nonagon is 140 degrees while its exterior angle is 40 degrees. The interior angle sum of a nonagon is 1260 degrees, which means that the sum of all of its interior angles is equal to 1260 degrees.
| Number of Sides (n) | Interior Angle Sum (sum of all interior angles) | Measure of Each Interior Angle | Measure of Each Exterior Angle |
|---|---|---|---|
| 9 | 1260 degrees | 140 degrees | 40 degrees |
Understanding the calculations of interior and exterior angles of a nonagon is essential in solving problems that involve this type of polygon.
Real-Life Examples of 9-Sided Polygons
Even though a 9-sided polygon (enneagon) is not a common shape that we often encounter in our daily lives, there are a few real-life examples where this unique shape can be found.
- Stop Sign: A stop sign is one of the most common examples of a regular enneagon that we come across on a daily basis. Its shape comprises nine equal sides and nine angles measuring 140 degrees each.
- Soccer Ball: Although the black and white patches may look like pentagons and hexagons, a soccer ball is actually made up of twelve regular pentagons and twenty regular hexagons, thus making a total of sixty panels. Out of these sixty panels, there are twelve enneagonal faces, and each of them forms a corner where five hexagons and five pentagons meet. So, the soccer ball has twelve 9-sided polygons.
- Nine-Sided Vases or Bowls: Some ceramic artists create vases or bowls that have nine flat sides. These types of vases or bowls are designed primarily for aesthetic purposes. You can use them as decorative items in your home or as a unique piece of art.
The nine-sided polygon’s unique shape also has some symbolism. In numerology, the number nine is considered a number of completion or the end of a cycle. This is because when you add any number to 9, the digital root will always be the same number. For example, 5+9=14, and if we add 1+4, we get 5, which is the same as the original number we added to 9.
Table: We can see the properties of a regular enneagon in the table below:
| Shape | Name | Number of Sides | Number of Vertices | Sum of Interior Angles |
|---|---|---|---|---|
| Regular | Enneagon | 9 | 9 | 1260° |
In conclusion, although a 9-sided polygon is not a common shape that we see on a daily basis, they do exist. We can find them in traffic signs, soccer balls, and vases. The enneagon’s unique shape, with its nine sides, has some symbolism and is considered a number of completion in numerology.
The History of Polygonal Shapes
Polygonal shapes have been studied and used in mathematics, art, and architecture for centuries. Throughout history, these shapes have been named and categorized by the number of sides and vertices they possess. From triangles to hexagons, to more complex shapes like a heptadecagon with seventeen sides, each polygon has unique characteristics and properties.
- The Greeks were the first to study the properties of polygonal shapes, and it was Euclid who systematized the study of geometry in his book “Elements” around 300 BC.
- Islamic mathematicians in the Middle Ages also studied polygonal shapes and expanded on the work of the Greeks.
- In the 17th century, Descartes introduced the concept of using coordinates to plot points on a graph, which led to the development of analytic geometry and the study of polygons in a new way.
The 9 Sided Polygon
A nine-sided polygon is called a nonagon or enneagon. The name derives from the Greek words “nona” meaning nine and “gon” meaning “angle” or “corner.”
Like other polygons, a nonagon has properties unique to its shape. The sum of all the interior angles of a nonagon is 1260 degrees, while each exterior angle is 40 degrees. It also has nine vertices and nine sides of equal length.
| Number of sides | Name of polygon |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 9 | Nonagon |
Nonagons can be found in nature and in various man-made structures, such as the wheels on a bicycle or a stop sign. They have also been used in art and design as a way to create intricacy and complexity in patterns and motifs.
Unique Characteristics of Polygons with Odd Number of Sides
Polygons are shapes that are made up of straight lines and angles, and they have a number of unique characteristics based on the number of sides they have. In particular, polygons with an odd number of sides have several distinctive properties that make them interesting to study. In this article, we will focus on the 9 sided polygon and what it is called, as well as explore the other unusual features of polygons with an odd number of sides.
The Name of a 9 Sided Polygon
A polygon with nine sides is called a nonagon or enneagon. The name is derived from the Greek words “nona” and “ennea,” which mean “nine.” These two terms can be used interchangeably to refer to a nine-sided polygon, although nonagon is the more commonly used name.
Unique Characteristics of Polygons with Odd Number of Sides
- Polygons with odd numbers of sides are symmetrical when the center point is selected as an axis of symmetry.
- They have an odd number of diagonals.
- The sum of their interior angles is always a multiple of 180 degrees.
These properties hold true for all odd-sided polygons, including nonagons. The symmetrical nature of these shapes makes them visually pleasing, while the odd number of diagonals and the formula for calculating interior angles make them mathematically interesting.
The Interior Angles of a Nonagon
The formula for calculating the sum of the interior angles of a polygon is (n-2) x 180 degrees, where n is the number of sides. Therefore, the sum of the angles of a nonagon is (9-2) x 180 = 1260 degrees. To find the measure of each individual angle, we divide the sum by the number of angles, which gives us 140 degrees per angle.
| Number of Sides | Sum of Interior Angles | Measure of Each Interior Angle |
|---|---|---|
| 3 | 180 | 60 |
| 4 | 360 | 90 |
| 5 | 540 | 108 |
| 6 | 720 | 120 |
| 7 | 900 | 128.57 |
| 8 | 1080 | 135 |
| 9 | 1260 | 140 |
As we can see from the table above, the measure of each interior angle increases as the number of sides of the polygon increases. This is intuitive, as a shape with more sides has more angles and each angle must be smaller to fit into the full polygon.
In conclusion, a nine-sided polygon is called a nonagon or enneagon. Polygons with odd numbers of sides, including nonagons, have several unique characteristics such as symmetry, an odd number of diagonals, and a specific formula for calculating interior angles. By understanding the properties of these shapes, we can gain a deeper appreciation for the complexity and beauty of mathematics.
Relations Between Polygonal Shapes and Symmetry
When it comes to polygons, there is a direct relationship between the number of sides and the amount of symmetry. Generally, the more sides a polygon has, the more symmetric it is. This symmetry is created by the equilibrium between the sides, angles, and vertices. Below, we will discuss this relationship further and dive into the specific properties of each polygon in relation to symmetry.
Number of Sides and Symmetry
- A 3-sided polygon, also known as a triangle, has 3 lines of symmetry, making it highly symmetric.
- A 4-sided polygon, or quadrilateral, can either have no lines of symmetry (such as a kite) or up to 2 lines of symmetry (such as a square or a rectangle).
- A 5-sided polygon, or pentagon, can have up to 5 lines of symmetry. However, if the sides are not equal in length or the angles are not equal, the number of lines of symmetry decreases.
- A 6-sided polygon, or hexagon, can have up to 6 lines of symmetry. But, similar to the pentagon, the number of lines of symmetry decreases if the sides and angles are not equal.
- A 7-sided polygon, also known as a heptagon, can have up to 7 lines of symmetry. And, if the sides are equal in length and the angles are equal, then a heptagon can have rotational symmetry. However, no matter how symmetric it is, it can not have reflection symmetry because it has an odd number of sides.
- An 8-sided polygon, or octagon, can have up to 8 lines of symmetry. And, if it is regular, then it can have both rotational and reflection symmetry.
- A 9-sided polygon, known as a nonagon, can have up to 9 lines of symmetry, making it highly symmetric.
Symmetry Properties of Polygons
Polygons with lines of symmetry can be categorized into two types: rotational and reflection symmetry. Rotational symmetry occurs when a polygon can be rotated by a certain degree and still appear the same. Reflection symmetry occurs when a polygon can be reflected over the line of symmetry and still appear the same.
Another property related to symmetry is the angle measure. For example, a regular polygon has equal angles, and an irregular polygon does not. The equilateral triangle has the same angle measure as a regular hexagon and a regular dodecagon has the same angle measure as a regular pentagon.
Conclusion
The number of sides of a polygon plays a significant role in its symmetry properties. As the number of sides increases, the number of lines of symmetry increases, making the polygon more symmetrical. Additionally, having equal sides and angles plays a crucial role in determining the number of lines of symmetry and the type of symmetry. By understanding the symmetry properties of polygons, we can better appreciate the beauty and intricacy of these shapes.
| Polygon Name | Type of Symmetry | Number of Lines of Symmetry |
|---|---|---|
| Triangle | Rotational symmetry | 3 |
| Quadrilateral | Reflection symmetry or no symmetry | 0-2 |
| Pentagon | Rotational symmetry | 0-5 |
| Hexagon | Rotational symmetry | 0-6 |
| Heptagon | Rotational symmetry | 0-7 |
| Octagon | Rotational and reflection symmetry (if regular) | 0-8 |
| Nonagon | Rotational symmetry | 0-9 |
Table: The relationship between the name of the polygon, the type of symmetry, and the number of lines of symmetry.
FAQs: What is a 9 sided polygon called?
Q: What is a polygon?
A: A polygon is a closed geometric shape with straight sides.
Q: What is a 9 sided polygon called?
A: A 9 sided polygon is called a nonagon.
Q: How many angles does a nonagon have?
A: A nonagon has nine angles.
Q: What is the sum of the angles in a nonagon?
A: The sum of the angles in a nonagon is 1260 degrees.
Q: Can a nonagon be a regular polygon?
A: Yes, a regular nonagon has nine congruent sides and angles.
Q: What are some real-life examples of a nonagon?
A: A baseball has a nonagon shape on it, and the Enneagram symbol is a nonagon.
Q: How do you calculate the interior angle of a nonagon?
A: You can calculate the interior angle of a nonagon by dividing 1260 degrees by 9, which equals 140 degrees.
Closing: Thanks for reading!
We hope you learned something new today about nonagons and their characteristics. Remember, a nonagon can be found in real-life objects and has nine angles and sides. If you have any further questions, don’t hesitate to come back and visit us again. Thanks for reading!