A Polygon With 100 Sides
Polygons
Polygons are defined equally aeroplane (two-dimensional) and closed shapes that are formed past joining three or more than line segments with each other. We tend to see polygons mostly while nosotros learn about geometry. In this lesson, we volition larn about polygons and their identification using charts in detail.
| 1. | What are Polygons? |
| 2. | Identification and Naming of Polygons |
| iii. | Departure Between Regular and Irregular Polygons |
| 4. | Angles in Regular Polygons |
| 5. | Polygons Formula |
| 6. | Polygons Worksheets |
| vii. | FAQs on Polygons |
What are Polygons?
In geometry, the definition of a polygon is given as a closed 2-dimensional effigy with three or more straight lines. The Greek word "Polygon" consists of Poly meaning "many" and gon meaning "angle". We encounter many unlike polygons effectually the states. For example, the shape of a honeycomb is a hexagon. Each polygon is different in structure, they are categorized based on the number of sides and their properties. Thus, all polygons are closed plane shapes.
Identification and Naming of Polygons
We tin can place a polygon by checking the following characteristics in a shape:
- It is a closed shape, that is, there is no cease that is left open in the shape. It ends and begins at the aforementioned point.
- It is a plane shape, that is, the shape is made of line segments or directly lines.
- It is a two-dimensional figure, that is, it has only two dimensions length and width. There is no depth or summit to it.
- The shape must accept 3 or more sides.
- The angles in the polygon may or may not be the same.
- The length of the sides of a polygon may or may not be the same.
In society to understand polygons and their naming convention meet the nautical chart given below.
Polygon Nautical chart
This chart shows the naming convention of polygons on the basis of the number of their sides. Each polygon is given a special name on the footing of its number of sides, such a manner that when the proper name of the polygon is written its 1 part is too influenced by the number of its sides. For example, the trigon, too known every bit the triangle is fabricated of two words "tri" which means three, and gon mean angles which refers that it is a shape having 3 angles.
Difference Between Regular and Irregular Polygon
A polygon tin be categorized every bit regular and irregular polygon based on the length of its sides. As the name suggests "regular" in regular polygon literally means a definite design that appears in the regular polygon while on the other hand "irregular" in irregular polygon means in that location is an irregularity that appears in a polygon. Let u.s.a. larn about them individually.
The difference between regular and irregular polygon is given as:
| Criterion of Difference | Regular Polygon | Irregular Polygon |
|---|---|---|
| Length of sides | Equal | Diff |
| Measurement of all interior angles | Equal | Unequal |
| Measurement of all outside angles | Equal | Diff |
Regular vs Irregular Polygons
It is said that equally per Euclidean Geometry, a polygon that is equiangular and equilateral is chosen a regular polygon while a polygon whose sides are non equiangular and equilateral is referred to as an irregular polygon. A regular polygon is e'er prefixed by the term "regular". Regular polygons are convex i.e., all the interior angles measure less than 180º.
In simple words, a regular polygon has all angles of the same measure at each vertex and all sides of the same length while a polygon that does not have sides of the aforementioned length and measurement of angles at each vertex different is referred to as an irregular polygon.
Because the below effigy of a regular hexagon, let us discuss the parts of a regular polygon:
- Vertices
- Sides
- Interior Angles
- Outside Angles
- Diagonals
Where,
- Vertices are A, B, C, D, E, and F
- Equal sides are AB, BC, CD, DE, EF, FA
- BE is the diagonal.
- All the interior angles are equal (represented by blueish color in the figure)
- All the exterior angles are equal (represented by yellow colour in the figure)
Angles in a Regular Polygon
As we learned to a higher place, there are two kinds of angles that can be institute in the instance of a regular polygon. They are:
- Interior Angles of a Polygon
- Exterior Angles of a Polygon
Interior Angles of a Polygon
The interior angles are formed betwixt the side by side sides inside the polygon and are equal to each other in the case of a regular polygon. The number of interior angles is equal to the number of sides. The value of an interior angle of a regular polygon tin be calculated if the number of sides of the regular polygon is known by using the following formula:
Interior angle = 180º(n-2)/n, where n is the number of sides
Outside Angles of a Polygon
Each exterior angle of a regular polygon is formed by extending one side of the polygon (either clockwise or anticlockwise) and then the angle between that extension and the adjacent side is measured. Each outside angle of a regular polygon is equal and the sum of the outside angles of a polygon is 360°. An exterior angle can be calculated if the number of sides of a regular polygon is known by using the following formula:
Exterior Angle = 360º/n, where northward is the number of sides
Important Notes
- Polygons are 2-D figures with more than 3 sides.
- Angles of a regular polygon tin can exist measured by using the following formulas:
Exterior Angle = 360º/n
Interior bending = 180º(n-two)/due north, where n refers to the number of sides. - The sum of interior and outside angles at a point is e'er 180º equally they class a linear pair of angles
- For an 'n'-sided polygon, the number of diagonals can be calculated with this formula, n(n-three)/2.
Polygon Formulas
There are 2 basic formulas for polygons listed below:
- Area of polygons
- Perimeter of polygons
Let the states learn nigh the above-listed two polygon formulas in item.
Area of Polygons
The area of a polygon is defined every bit the measurement of infinite enclosed inside a polygon. The area of polygons can exist found past different formulas depending upon whether the polygon is a regular or an irregular polygon. For instance, a triangle is a three-sided polygon which is known as a trigon. The formula for computing the area of the trigon (triangle) is half the production of the base and height of the triangle. It is expressed in terms of yard2, cmii, ftii.
Perimeter of Polygons
The perimeter of a polygon is defined as the distance around a polygon which tin can be obtained by summing upward the length of all given sides.
The perimeter of polygon formula = Length of Side 1 + Length of Side 2 + Length of Side 3...+ Length of side N (for an Due north-sided polygon). It is expressed in terms of units such equally meters, cm, feet, etc.
Polygons Worksheets
The polygons worksheets will assistance children recognize more shapes and patterns in real life. Information technology likewise develops the base of understanding and establishing the necessary basic background for geometry.
Download Polygons Worksheet PDFs
These math worksheets should be practiced regularly and are costless to download in PDF formats.
☛ Topics Related to Polygons
Check out these interesting articles to know more about polygon and its related topics.
- Polygon Reckoner
- eleven Sided Polygon
- Pentagon Shape
- Hexagon
Polygons Examples
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Example 1: Assistance Andrea in identifying the shape of polygons out of the given options.
Solution: The watermelon slice has ane curved side. A polygon should accept only direct lines. Thus, the slice of watermelon is non a polygon. The dice is non a polygon because it is iii-dimensional. It is a polyhedron. A polygon does not have whatsoever open up ends. Therefore, the open-ended shape is non a polygon. Hence, the polygons are:
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Practise Questions on Polygons
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FAQs on Polygons
What are Polygons in Math?
The airplane airtight shapes that comprise iii or more than line segments are referred to as polygons. The world polygon as the name suggests is made of two words "poly" and "gon" where the discussion poly means "many" and the gon means "angles". Polygons are ever 2-dimensional in shape.
How to Identify a Polygon?
A shape is a polygon if it has the following characteristics:
- The shape must exist a airtight shape, that is, information technology must end and begin at the same indicate.
- The shape is a plane shape, that is, the shape is fabricated of line segments or straight lines.
- The shape must exist a two-dimensional figure, that is, it must have but 2 dimensions length and width.
- It must have three or more sides.
- The angles in the polygon may or may not be the aforementioned.
- The length of the side of a polygon may or may not exist the aforementioned.
What is the Divergence Between a Regular and Irregular Polygon?
A polygon whose length of all sides is equal with equal angles at each vertex is chosen a regular polygon, while an irregular polygon is a polygon whose sides are non equal and angles differ from each other. These are the parameters that help us in differentiating between a regular and an irregular polygon.
☛ Also Check:
- Types of Polygon
How do you know if a Polygon is Regular?
Any polygon is a regular polygon if information technology satisfies the below three criteria:
- The length of all its sides must exist equal.
- All interior angles must measure the same.
- All the outside angles must measure the aforementioned.
What is the Interior Angle of Regular Polygon?
The angle that is formed by adjacent sides inside the polygon is referred to as the interior angle. The values of all the interior angles in a regular polygon are equal to each other. The value of an interior bending of a regular polygon tin be calculated by using the following formula, interior angle = 180º(northward-2)/north, where n is the number of sides.
Is a Circle Considered a Polygon?
No, a circle is not considered a polygon considering it is not made up of iii or more straight lines or line segments. Information technology does not fulfill the criterion which can be used to identify a polygon, as information technology neither has three or more than sides nor it shows any angles. Thus, we say the circumvolve is non a polygon.
What is an xi Sided Polygon Called?
An 11 sided polygon is referred to as Hendecagon. It is derived from two Greek words "Hendeka" which means eleven and "gon" which means angles. Both the words cumulatively refer to the shape beingness an xi-sided polygon.
How are Polygons Named?
The name of each polygon is made of ii words. The starting time role of the word is influenced past the Greek meaning of the number of sides it possesses and it is suffixed by the word gon. For instance, the word "Hexagon" is fabricated of two words "hex" and "gon". The word "hex" means the number half dozen and "gon" means the angles. The words "Triangle" and "Quadrilateral" stand as an exception in this case as they are non given equally per the nomenclature.
Are Polygons Always Closed Shapes?
Yes, polygons are always closed shapes as they are made of three or more direct lines which begin and start at the same point. For whatever shape to be a polygon it is necessary that it is a closed shape. This is also 1 of the most important criteria used to place a shape every bit a polygon.
What is the Area of Polygon Shape?
The total space enclosed by a polygon in a ii-dimensional plane is defined as the expanse of a polygon. We write the unit of measurement of surface area of the polygon as foursquare units such as (meterstwo or centimeters2, etc.) or USCS units (inches or feet, etc).
What is the Perimeter of Polygon Shape?
The perimeter of a polygon is divers as the total length of the boundary of the polygon in a two-dimensional plane. Units for polygons perimeter is expressed as centimeters or inches or feet respectively.
Are All Triangles Polygons?
Aye, all triangles are polygons as they follow all the criteria of being a polygon. In the case of any triangle, whether equilateral triangle, isosceles triangle, or scalene triangle, the following criteria are always satisfied:
- The shape ends and begins at the same indicate.
- It is fabricated of line segments or straight lines.
- It has only two dimensions that are length and width.
- It has three sides.
- The angles may or may not be the aforementioned.
- The length of the side of a polygon may or may non be the aforementioned.
Thus the to a higher place-given points evidence that all triangles are polygons.
A Polygon With 100 Sides,
Source: https://www.cuemath.com/geometry/polygons/
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