CLASS-7
POLYGON

POLYGON -

A polygon is a two-dimensional (2D) shape with straight sides. It is a closed figure, meaning that all its sides connect to form a complete boundary. Polygons are classified based on the number of sides they have, and they are one of the most fundamental objects in geometry.

A) Key Characteristics of Polygons:-

  1. Sides (Edges):- The straight line segments that form the boundary of the polygon.
  2. Vertices:- The points where two sides meet.
  3. Interior Angles:- The angles formed inside the polygon at each vertex.
  4. Convex vs. Concave:- 

        a) Convex polygon:- All interior angles are less than 180°, and no sides are bent inward.

     b) Concave polygon:- One or more interior angles are greater than 180°, and some sides bend inward.


B) Classification by Number of Sides:-

  • Triangle (3 sides)
  • Quadrilateral (4 sides)
  • Pentagon (5 sides)
  • Hexagon (6 sides)
  • Heptagon (7 sides)
  • Octagon (8 sides)
  • Nonagon (9 sides)
  • Decagon (10 sides)
  • n-gon: A polygon with n sides.


C) Types of Polygons:-

  1. Regular Polygon:- A polygon where all sides are equal in length, and all interior angles are equal.

       Example:- A square (regular quadrilateral), equilateral triangle (regular triangle).

  2. Irregular Polygon:- A polygon where the sides and angles are not all equal.

       Example:- A rectangle (irregular quadrilateral), scalene triangle (irregular triangle).


D) Properties:-

  • Sum of Interior Angles:- 

  The sum of the interior angles of a polygon with nnn sides is given by:-

    Sum of interior angles = (n−2) × 180∘

   For example, the sum of the interior angles of a quadrilateral (4 sides) is (4−2) × 180∘ = 360∘

  • Each Interior Angle of a Regular Polygon:- 

   In a regular polygon with n sides, each interior angle can be calculated as:

                                 (n−2) × 180∘

      Each interior angle = ---------------

                                      n

  • Exterior Angles:-

     The exterior angles of any polygon, no matter the number of sides, always add up to 360∘.


E) Examples of Common Polygons:-

  • Triangle (3 sides):- The simplest polygon, where the sum of interior angles is always 180∘.
  • Square (4 sides):- A regular quadrilateral, where each angle is 90∘.
  • Pentagon (5 sides):- A polygon where the sum of the interior angles is 540∘.
  • Hexagon (6 sides):- A polygon often found in nature, such as in honeycombs. The sum of the interior angles is 720∘.

      Polygons are widely used in geometry to study properties of shapes and are also important in fields such as architecture, art, and computer graphics.