Regular Polygon

an n-sided polygon with all of its sides the same length and symmetrically positioned around a common center is known as a regular polygon (n=1) (i.e., the polygon is both equiangular and equilateral). Only a few regular polygons may be “constructed” using the classical Greek instruments of the compass and straightedge, and these are only certain regular polygons.

When we talk about ordinary 3- and 4-polygons, we’re talking about equilateral triangles and squares, respectively. In the lack of specified wording, the terminology for polygons with n>=5 sides (e.g., pentagon, hexagon, heptagon, and so on) can refer to either regular or non-regular polygons. However, in the absence of precise wording, the terms normally refer to regular polygons.

Polygons

In geometry, a polygon is defined as a closed two-dimensional object with three or more straight lines that are closed on all sides. The Greek word “Polygon” is made up of the words Poly, which means “many,” and gon, which means “angle.” Around us, we may see a variety of polygon shapes. The shape of a honeycomb, for example, is hexagonal. Each polygon has a unique structure, and they are divided into groups based on the number of sides and the features they possess. As a result, all polygons are plane objects that are closed at one end.

Identification and Naming of Polygons

Checking the following properties of a shape can help us determine whether it is a polygon.

• It is a closed shape, which means that there is no end to the shape that is left unfinished. It both finishes and begins at the same place in the story.

• It is a plane shape, which means that the shape is made up of line segments or straight lines, rather than curved lines.

• It is a two-dimensional figure, which means that it only has two dimensions, which are length and width. There isn’t any depth or height to it all.

• The shape must have three or more sides in order to be considered.

• It is possible that the angles in the polygon are not the same.

• Polygonal sides may or may not have the same length, depending on how they are constructed. 

Regular vs Irregular Polygons

An irregular polygon is defined as a polygon whose sides are not equal in length and width, according to Euclidean Geometry. A regular polygon is defined as a polygon whose sides are equal in length and width, according to Euclidean Geometry. A regular polygon is always preceded by the word “regular” to indicate that it is regular. Regular polygons are convex, which means that all of the internal angles are smaller than 180 degrees. 

In layman’s terms, a regular polygon has all angles at each vertex that are the same measure and all sides that are the same length, whereas an irregular polygon does not have sides that are the same length and angles at each vertex that are different measurements.

Let us look at a normal hexagon and analyze its parts:

 Where, 

• The vertices are denoted by the letters A, B, C, D, E, and F.

• AB, BC, CD, DE, EF, and FA are the equal sides.

• The diagonal is represented by the letter BE.

• All of the inner angles are the same size.

• All of the external angles are the same size. 

Polygon Formulas

 Area of Polygons

It is defined as the measurement of space encompassed within a polygon by the term “area of the polygon.” It is possible to calculate the area of polygons using a variety of formulas, depending on whether the polygon is regular or irregular. For example, a triangle is a three-sided polygon that is referred to as a trigon in mathematics. A trigon (triangle) has an area equal to half the product of its base and height, which is the formula for determining the area of the triangle. It is expressed in terms of m.2, cm2, ft2.

 Perimeter of Polygons

The perimeter of a polygon is defined as the distance around a polygon that may be calculated by adding together the lengths of all of the polygon’s sides.

The perimeter of a polygon is equal to the sum of the lengths of each of the polygon’s sides (for an N-sided polygon). It is stated in terms of measurement units such as meters, centimeters, feet, and so on.

Important Notes

 Polygons are 2-D figures that have more than three sides on each side.

• It is possible to calculate the angles of a regular polygon using the following formulas:

• The outside angle is equal to 360o/n.

• The interior angle is equal to 180o(n-2)/n, where n is the number of sides on the triangle.

• Because they are formed by a linear pair of angles, the total of inner and exterior angles at a point is always 180o.

• It is possible to compute the number of diagonals in an ‘n’-sided polygon by using the following formula: n(n-3)/2.

CONCLUSION

A polygon is a closed form with straight sides that is used in geometry. Polygons include shapes such as rectangles, triangles, hexagons, and octagons, to name a few. The word polygon derives from the Greeks, who also established most of the words in geometry that we use today.

A simple polygon is a polygon that does not overlap with itself in any way. Mathematicians are frequently simply concerned with the polygonal chains that determine the boundaries of simple polygons, and they define a polygon in this manner. In some cases, it is permissible for a polygonal boundary to cross over itself, resulting in star polygons and other self-intersecting polygons.