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When it comes to Euclidean geometry, the concept of a polygon is critical. Geometric polygons are closed plane objects with all of their sides being made out of line segments. Each side should bisect exactly two other sides, but only at their endpoints, in order to be considered complete. The sides of polygons should be noncollinear and have a common endpoint unless otherwise specified. As previously stated, there are various sorts of polygons, and each polygon is often named according to the number of sides it has.
It is important to note that a polygon with n sides (=12) is referred to as an n-gon.
Polygonal Classification with Detailed Description
Triangles or polygons with three sides
As we all know, polygons can have many sides, but a triangle is a three-sided polygon that has three sides. There are various different sorts of triangles, and we will go through each of them briefly:
Equilateral Triangle: In this triangle, all of the sides are equal in length, and all of the interior angles are 60 degrees.
When a triangle is isosceles, it has two equally long sides and a third side that has a different length from the other two. Any two of the three internal angles that are presented are equivalent.
The Scalene Triangle is distinguished by the fact that each of its three sides and angles is different.
However, it is important to note that all of the internal angles of a triangle sum up to 180°, therefore it is possible to characterize triangles in terms of their internal angles as well.
An acute triangle is a triangle with internal angles that are fewer than 90 degrees on the diagonal. Obtuse triangles, on the other hand, are made up of a right triangle with one obtuse angle and two acute angles on either side. A right-angled triangle is a triangle that has a right angle at one of its sides.
Each of these triangles can then be classed as either equilateral, isosceles, or scalene, depending on their shape.
Quadrilaterals are polygons with four sides
Quadrilaterals, quadrangles, and tetragons are all terms used to describe four-sided polygons. A quadrilateral is the most widely used term to describe this shape.
Various figures such as the square, the rectangle, the rhombus, and the parallelogram are all included in the definition of quadrilaterals. The trapezium is a quadrilateral as well as a rectangle.
Whatever the figure, the internal angles of all quadrilaterals add up to 360°, regardless of the figure.
The square has four equal-length sides and four internal right angles, making it a perfect shape.
Square: There are four internal right angles in this shape, and the opposite sides are all the same length.
Parallelograms are shapes in which the opposite sides of the figure are parallel and the opposite angles are equal on the opposite sides.
Rhombus: This figure is a sort of parallelogram that is distinct from the others. In this case, the length of all four sides is the same.
Trapezium: This form is also referred to as a trapezoid in some circles. Two of the sides of this figure are parallel, however, the other two sides of this figure are not parallel. The sides and angles are all uneven in length and width.
A unique sort of trapezium, the Isosceles Trapezium is described below. The sides are parallel to one another, and the base angles are all the same. This directly implies that the length of non-parallel sides is the same as the length of parallel sides.
Kite: There are two pairs of adjacent sides that are the same length in this case. The presence of axes of symmetry in the shape is also a defining aspect of the design.
Polygons are classified into several types
Polygons can be classified into the following classes based on the sides and angles of a closed plane figure:
A Regular Polygon is a polygon with a regular shape.
A polygon with Irregular Shapes
A polygon with a concave surface
A convex polygon is a polygon with a convex shape.
The Different Types of Polygons and Their Characteristics
A polygon with Equal Sides and Interior Angles: If the sides and interior angles of a polygon are all of the same lengths, the polygon is considered to be regular. In geometry, a regular polygon is defined as a polygon in which all of the sides and all of the angles are identical. Plane forms such as the square, rhombus, equilateral triangle, and other similar shapes are instances of regular polygons.
When all of the sides and interior angles of a polygon do not measure exactly the same length, the polygon is referred to as an irregular polygon, and it is defined as follows: A rectangle, a kite, a scalene triangle, and other irregular polygons are examples of irregular polygons.
Concave Polygon: A concave polygon is defined as a polygon whose interior angles measure more than 180° on one or more of its interior angles. A concave polygon can have as few as four sides as necessary to be considered concave. The vertex will be oriented so that it points toward the inside of the polygon.
If the interior angles of a polygon are all strictly less than 180°, the polygon is said to be convex, and the exterior angles are called oblique. The vertex of the shape is the point that extends outwardly from the center of the shape.
Conclusion
As previously said, polygons are classed according to the number of sides, shape, angle, and features they possess. As a result, we’ve compiled a list of the most important characteristics of polygons that will assist you in quickly identifying the different types of polygons.
In an n-sided polygon, the sum of all the interior angles is equal to (n – 2) 180°.
The angle measurement of each interior angle of an n-sided regular polygon is (n–2)180°/n, where n is the number of sides of the polygon.
The angle measurement of each exterior angle of an n-sided regular polygon is 360°/n, which is the reciprocal of the number of sides.
When there are n sides to a polygon, the number of diagonals in the polygon is equal to n(n–3)/2.
n – 2 triangles are constructed by joining the diagonals of a polygon from one corner to the other corner of the polygon.
