CLASS-7
POLYGON - NONAGONS
NONAGONS -
A nonagon is a polygon with nine sides and nine angles. Here are some key properties and details about nonagons:
Types of Nonagons:-
- Regular Nonagon:- All sides are of equal length.All internal angles are equal, with each angle measuring 140°.A regular nonagon has symmetrical properties and can be inscribed in a circle.
- Irregular Nonagon:- The sides and angles are not necessarily equal, resulting in an asymmetrical shape.
Area Formula for a Regular Nonagon:-
The area A of a regular nonagon with side length s can be calculated using this formula:
9 π
A = ------ s²cot (-----)
4 9
This formula helps calculate the area based on the side length and the cotangent of the angle.
Other Properties:-
- The perimeter of a regular nonagon is simply nine times the length of one side:-
Perimeter = 9 × s
- The sum of the internal angles of any nonagon is always 1,260°, regardless of whether it's regular or irregular.
Examples of Nonagons in Real Life:-
- Architecture:- Nonagons can sometimes be found in architectural designs, especially in floor plans and towers, as the shape is visually appealing and unique.
- Decorative Art:- Nonagonal patterns might appear in tiling, mosaics, and other forms of design, especially in traditional or geometric art.