CLASS-7
POLYGON - HEPTAGON

HEPTAGONS -

A heptagon is a polygon with seven sides and seven angles. Here are the key properties and details about heptagons:-

Types of Heptagons:-

1. Regular Heptagon:- All sides are equal in length.All internal angles are equal, with each internal angle measuring approximately 128.57°.A regular heptagon has symmetrical properties, and it can be inscribed in a circle.
2. Irregular Heptagon:- The sides and angles can vary in length and measure, making it an asymmetrical figure.

Area Formula for a Regular Heptagon:-

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

                   7               π

           A = ------ s²cot⁡ (------) 

                   4               7

However, this can also be simplified using approximations when needed.

Other Properties:-

• The perimeter of a regular heptagon is simply seven times the length of one side: 

            Perimeter = 7 × s 

• The sum of the internal angles of any heptagon is always 900°, regardless of whether it's regular or irregular.

Examples of Heptagons in Real Life:-

• Coins:- Some coins, like the British 50p coin, are designed in a rounded heptagonal shape for easy recognition.
• Architecture and art:- Heptagonal shapes are sometimes used in designs to symbolize uniqueness or to achieve aesthetic harmony.