CLASS-7
POLYGON - OCTAGONS

OCTAGON -

An octagon is a polygon with eight sides and eight angles. Here are the key characteristics and details about octagons:-

Types of Octagons:-

1. Regular Octagon:- All eight sides are of equal length.All internal angles are equal, with each angle measuring 135°.A regular octagon can be inscribed in a circle, meaning all its vertices touch the circumference.
2. Irregular Octagon:- The sides and angles can differ in length and measure, leading to asymmetry.

Area Formula for a Regular Octagon:-

The area A of a regular octagon with side length sss can be calculated using the following formula:

                A = 2 (1 + √2) s²

This formula helps calculate the area based on the side length.

Other Properties:-

• The perimeter of a regular octagon is eight times the side length:

                  Perimeter = 8 × s

• The sum of the internal angles of any octagon is always 1,080°, regardless of whether it's regular or irregular.

Examples of Octagons in Real Life:-

• Stop Signs:- The most iconic example is the stop sign, which is a regular octagon used for road signage worldwide.
• Architecture:- Octagonal shapes are common in design and architecture, such as in domes, towers, and floor plans for religious buildings.
• Tiles:- Octagonal tiles are often used in flooring and mosaics, allowing for interesting patterns and symmetry.