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VOOZH | about |
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VOOZH | about |
Polygons are closed two-dimensional shapes made with three or more lines, where each line intersects at vertices. Polygons can have various numbers of sides, such as three (triangles), four (quadrilaterals), and more.
In this article, we will learn about the polygon definition, the characteristics of the polygon, the types of polygons and others in detail.
Table of Content
A polygon is a two-dimensional, closed shape with three or more straight sides. The name of a polygon indicates how many sides it has. For example, a triangle has three sides and a quadrilateral has four sides.
Polygons have the following characteristics:
Different polygon formulas are added in the table below:
| Sum of Interior Angles of a Polygon | (n-2)×180° |
|---|---|
| Interior Angle of a Regular Polygon | {(n-2)×180°}/n |
| Exterior Angle of a Regular Polygon | 360°/n |
| Perimeter of an n-sided Regular Polygon | n × s |
| Area of an n-sided Regular Polygon | (n × s × Apothem)/2 = (Perimeter × Apothem)/2 = (l/2)×tan(180°/n) |
where,
Below are some types of polygons based on the number of sides of a polygon,
Number of Sides | Name of Polygon | Figure |
|---|---|---|
3 | ||
4 | ||
5 | ||
6 | Hexagon | |
7 | ||
8 | ||
9 | ||
10 | Decagon |
Based on measure of angles and the sides of a polygon, they are classified into the following types
A polygon is said to be a regular polygon if it has all the interior angles and the sides are of the same measure. The regular polygon are shown in the image added below:
A polygon is said to be a irregular polygon if it has all the interior angles and the sides have different values. The irregular polygon are shown in the image added below:
A concave polygon is a polygon that has at least one interior angle greater than 180 degrees, i.e., a reflex angle. The concave polygon are shown in the image added below:
A convex polygon is a polygon that has all the interior angles of a polygon less than 180 degrees. The convex polygon are shown in the image added below:
An equilateral polygon is a polygon whose all sides measure the same.
An equiangular polygon is a polygon whose all angles measure the same.
Various properties of polygon are:
Let's solve some example problems based on the Polygon Formulas.
Example 1: Calculate the perimeter and value of one interior angle of a regular heptagon whose side length is 6 cm.
Solution:
Polygon is an heptagon. So, number of sides (n) = 7
Length of each side (s) = 6 cm
We know that,
Perimeter of the heptagon (P) = n × s
P = 7 × 6
= 42 cm
Now, find each interior angle by using the polygon formula,
Interior Angle = [(n-2)180°]/n
= [(7 - 2)180°]/7
= (5 × 180°)/7
= 128.57°
Therefore, perimeter of the given heptagon is 42 cm and the value of each internal angle is 128.57°.
Example 2: Calculate the measure of one interior angle and the number of diagonals of a regular decagon.
Solution:
Polygon is a decagon. So, number of sides (n) = 10
Now, to find each interior angle by using the polygon formula,
Interior Angle = [(n-2)180°]/n
= [(10 - 2)180°]/10
= (8 × 180°)/10
= 144°
We know that,
Number of diagonals in a n-sided polygon = n(n-3)/2
= 10(10 - 3)/2
= 10(7)/2 = 35.
Therefore, value of each internal angle of a regular decagon is 144° the number of diagonals is 35.
Example 3: Calculate the sum of interior angles of a hexagon using the polygon formula.
Solution:
Polygon is a hexagon. So, number of sides (n) = 6
We know that,
Sum of interior angles of a polygon = (n-2)×180°
= (6-2)×180°
= 4×180° = 720°.
Hence, sum of interior angles of a hexagon is 720°.
Example 4: Calculate the measures of one exterior angle and the perimeter of a regular pentagon whose side length is 9 inches.
Solution:
Polygon is a pentagon. So, number of sides (n) = 5
We know that,
Length of each side (s) = 9 inches
We know that,
Perimeter of the pentagon (P) = n × s
P = 5 × 9
= 45 inches
Each exterior angle of a regular polygon = 360°/n
= 360°/5 = 72°.
Hence, measures of one exterior angle and the perimeter of a regular pentagon are 72° and 45 inches, respectively.
