CLASS-7
POLYGON - HEXAGONS

HEXAGONS -

A hexagon is a polygon with six sides and six angles. Here are some key features and properties of hexagons:

Area Formula for a Regular Hexagon:-

1. Regular Hexagon:- All six sides are equal in length.All internal angles are equal, with each angle measuring 120°. A regular hexagon has perfect rotational symmetry and can be inscribed in a circle. It is a common natural shape (e.g., honeycomb cells).
2. Irregular Hexagon:- The sides and angles can differ, making it an asymmetrical figure.

Types of Hexagons:-

The area A of a regular hexagon with side length s can be calculated using the formula:-

                            3√3

                     A = ------ s²

                             2

This formula is derived by dividing the hexagon into six equilateral triangles.

Other Properties:-

• The perimeter of a regular hexagon is simply six times the length of one side:-

                  Perimeter = 6 × s 

• The internal angles of any hexagon sum up to 720°.

Examples of Hexagons in Real Life:-

• Honeycombs:- Bees build their hives in hexagonal cells because this shape efficiently uses space and materials.
• Tiling and tessellations:- Hexagons are commonly used in tiling because they can cover a plane without any gaps.
• Stop signs:- While not a hexagon, the octagon shape of a stop sign shows how similar polygons are often used in signs for easy recognition.