9.1  Polygons

A polygon is an enclosed figure on a plane bounded by \(3\) or more straight sides.

The relationship between the number of sides, vertices and diagonals of a polygon:

For a polygon,

  • number of vertices \(=\) number of sides

The number of diagonals of a polygon having \(n\) sides can be calculated by using the following formula.

\(\begin{aligned} &\space\text{Number of diagonals} \\\\&=\dfrac{n(n-3)}{2} \end{aligned}\)


The number of vertices for a polygon is \(9\).


(i) the number of sides

(ii) the number of diagonals


Noted that,

number of vertices \(=\) number of sides.

Thus, the number of sides is \(9\).


Noted that \(n=9\).

\(\begin{aligned} &\space\text{Number of diagonals} \\\\&=\dfrac{n(n-3)}{2} \\\\&=\dfrac{9(9-3)}{2} \\\\&=27. \end{aligned}\)

Draw, label and name a polygon:
  • A polygon is named according to the number of its sides.

Steps to draw a polygon.

  1. Identify the number of sides of the polygon.
  2. Mark points equal in number to the number of sides.
  3. Join all the points with straight lines to form a closed figure.
  4. Label the vertices and name the polygon.
  • The vertices of a polygon are usually labelled in alphabetical order and the polygon is named either clockwise or anticlockwise of the vertices.