Regular Polygon

Definition of a polygon: A polygon is a closed 2-dimensional shape with three angles and 3 straight sides; it can have five sides or more than that too. The name “polygon” means “many angles” because all the simple polygons have as many sides as angles. With three internal angles, the triangle is the simplest polygon. As a result, there are three sides to it.

Polygons with a large number of sides can appear to be circles, even if they aren’t. Now that you have understood the definition of a polygon, let’s learn in detail about regular polygon types and the properties of a polygon. 

What is a regular polygon?

The smooth, straight-sided, closed object should also have another property to be a regular polygon. Every internal and exterior angle in a regular polygon is equal to every other exterior and interior angle, and each side is, in fact, the same length as the other side.

Know the Comparison Between Regular and Irregular Polygon

Regular polygon means “a certain pattern that arises in the regular polygon,” while irregular polygon means “a polygon with an irregularity,” as the name implies.

Types of Polygons

Different types of polygons are as follows:

1. Concave Polygon: This type of polygon is one with at least one interior angle greater than 180 degrees.

2. Convex Polygon: A convex polygon is one in which each internal angle is less than 180 degrees.

3. Regular Polygon: If a polygon is equiangular and equilateral, it is considered to be regular.

4. Irregular Polygon: This kind of polygon refers to the one with sides that are not equiangular and equilateral.

5. Equilateral Polygon: If all of the sides of a polygon are equal, it is said to be equilateral. Examples of the equilateral polygon are the equilateral triangle, rhombus, and square.

6. Equiangular Polygon: If all of the angles in a polygon are equal, it is said to be equiangular. Examples of equiangular polygons are the equilateral triangle and a square.

Types of Polygons Based on the Number of Sides

1. Triangle (Trigon)

The triangle is a three-sided polygon. These trigons or triangles are divided into several groups, including:

• Scalene Triangle: A scalene triangle is a triangle with all three sides having distinct lengths.

• Isosceles Triangle: An isosceles triangle is defined as a triangle with two sides of equal length.

• Equilateral Triangle: A triangle having all three sides equivalent is called an equilateral triangle. In addition, the angles of an equilateral triangle are all 60 degrees.

A triangle’s internal angles add up to 180 degrees.

2. Quadrilateral

A quadrilateral, sometimes known as a quadrangle, is a four-sided polygon. Quadrilaterals come in a variety of shapes and sizes. Square, rectangle, rhombus, parallelogram, and kite are examples of polygons. A quadrilateral’s interior angles add up to 360 degrees.

3. Pentagon

The Pentagon is a polygon with five sides. The points of five-line segments in the same plane are joined to form a pentagon.

Each of the Polygon’s five sides is the same length as a regular pentagon. An irregular pentagon is one in which the lengths of the sides are not equal. The total of a pentagon’s internal angles is 540.

4. Hexagon

A polygon with 6 sides and 6 vertices is known as a hexagon. All six sides of a regular hexagon are the same length. Its inner and exterior angles are also of identical magnitude. The total of a hexagon’s internal angles is 720.

Properties of Polygons

The following are the properties of polygons:

• A polygon has two kinds of angles, namely external and internal.

• Interior angles are the angles created at the vertices of a polygon.

• The internal angle of a polygon is the angle formed by two adjacent sides of the polygon. The angle measured at the inside section of a polygon is called the interior angle.

• Exterior angles are the angles created when one of the polygon’s sides is extended outside the polygon. It’s next to (the side of) the internal angle.

• The sides and interior angles of a regular polygon are all equal.

• The bisectors of the inner angles meet in the centre of a regular polygon.

• All perpendiculars drawn from the centre of a regular polygon to its sides are equal.

• The inscribed and circumscribed circles share the same centre as a regular polygon.

• Straight lines formed from a regular polygon’s centre to its vertices divide it into isosceles triangles.

Parts of Regular Polygons

As simple as they are, regular polygons still have six parts:

• Exterior Angles of a Regular Polygon

The outside angles of every basic polygon add up to 360 degrees since a trip around the polygon completes a revolution or returns you to your starting position.

• Regular Polygon Interior Angles

The hexagon’s interior is located between the hexagon’s sides, where the interior angles are located. The hexagon’s exterior is located outside its sides. This becomes critical when dealing with complex polygons, such as a star-shaped polygon (a pentagram, for example).

• Diagonal of a Polygon

To build diagonals, connect any non-adjacent vertices in the hexagon’s interior. Diagonals can be used to divide any simple polygon into triangles. By drawing three diagonals, we can make a minimum of four triangles in our hexagon; each triangle has interior angles that add up to 180°; therefore, the sum of the internal angles of a regular hexagon is 4 x 180 = 720°.

Conclusion

That’s all about the definition of polygon and its properties. You now have everything you need to identify polygons, distinguish regular from irregular polygons, name regular polygons and recognise them by their properties, list the parts of regular polygons, and calculate the sums of the interior angles of polygons. Regular, irregular, convex, and concave polygons are all possible. We can categorise them based on the number of sides and angles they have.