Regular Polygon

A regular polygon is a polygon that has all its sides equal in length and all its angles equal in measure. In simpler terms, a regular polygon is a shape with equal sides and equal angles. Let's delve into the details of regular polygons:

Key Points:

- Sides and Angles: In a regular polygon, all sides are of equal length and all angles are of equal measure. This means that if you know the number of sides a regular polygon has, you can easily calculate the interior and exterior angles.

- Examples: Some common examples of regular polygons include equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on.

- Properties: Regular polygons have a center called the circumcenter, which is equidistant from all vertices. The radius of the circumcircle passing through all vertices is known as the circumradius.

- Area: The formula to calculate the area of a regular polygon is (1/2) * perimeter * apothem, where the apothem is the distance from the center of the polygon to the midpoint of a side.

- Applications: Regular polygons are commonly seen in architecture, design, and nature. They are used in various fields for their symmetry and aesthetic appeal.

Regular polygons are fundamental shapes with unique properties that make them interesting and important in mathematics and other disciplines. Understanding their characteristics can help in solving problems and exploring the beauty of geometric shapes.

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