CLASS-7
POLYGON - DECAGONS

DECAGONS -

A decagon is a polygon with ten sides and ten angles. Here are the key properties and details about decagons:

Types of Decagons:-

1. Regular Decagon:- All ten sides are of equal length.All internal angles are equal, with each angle measuring 144°.A regular decagon has symmetrical properties and can be inscribed in a circle.
2. Irregular Decagon:- The sides and angles can vary, resulting in an asymmetrical shape.

Area Formula for a Regular Decagon:-

The area A of a regular decagon with side length s can be calculated using this formula:

                    5              π  

            A = ------ s²cot ⁡(-----)

                    2              10

This formula computes the area based on the side length and the cotangent of the angle.

Other Properties:-

• The perimeter of a regular decagon is ten times the length of one side:

               Perimeter = 10 x s

• The sum of the internal angles of any decagon is always 1,440°, whether it is regular or irregular.

Examples of Decagons in Real Life:-

• Coins:- Some coins are designed with decagonal shapes for easy handling and recognition.
• Architecture:-  Decagonal shapes can sometimes be found in architectural designs for both aesthetics and functionality.
• Decorative art and tiling:-  Decagons are often used in tiling patterns and artwork for their symmetry and appeal.