A polygon with all its sides and all its angles equal is called a regular polygon. Regular polygons have several distinctive properties that set them apart from other polygons. Let's delve into the details of regular polygons below:

Definition:
A regular polygon is a polygon that has equal sides and equal angles. In other words, all the sides and angles of a regular polygon are congruent.

Key Properties of Regular Polygons:
Regular polygons possess several important properties that make them unique:

Equal Sides:
In a regular polygon, all the sides are the same length. This means that the distance between any two consecutive vertices is constant throughout the polygon.

Equal Angles:
All the interior angles of a regular polygon are congruent. This means that each angle formed by any two consecutive sides is the same in measure.

Examples of Regular Polygons:
There are various examples of regular polygons, each with its own distinctive characteristics:

Equilateral Triangle:
An equilateral triangle is a regular polygon with three equal sides and three equal angles, each measuring 60 degrees.

Square:
A square is a regular polygon with four equal sides and four right angles, each measuring 90 degrees.

Pentagon:
A regular pentagon is a polygon with five equal sides and five interior angles, each measuring 108 degrees.

Hexagon:
A regular hexagon has six equal sides and six interior angles, each measuring 120 degrees.

Octagon:
An octagon is a regular polygon with eight equal sides and eight interior angles, each measuring 135 degrees.

General Formula:
The sum of the interior angles of a regular polygon can be calculated using the formula:

Sum of Interior Angles = (n - 2) * 180 degrees

Where 'n' represents the number of sides in the regular polygon.

Applications:
Regular polygons are used in various fields, including mathematics, architecture, and design. They possess symmetry and aesthetic appeal, making them a popular choice in art and construction.

Conclusion:
A regular polygon is a polygon with all its sides and angles equal. It exhibits unique properties and can be found in various shapes, from triangles to polygons with numerous sides. Understanding regular polygons is essential in geometry and has practical applications in various fields.

Square..