Polygons

9.1

Polygons

Definition

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,

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

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

Example

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

Find:

(i) the number of sides

(ii) the number of diagonals

(i)

Noted that,

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

Thus, the number of sides is \(9\).

(ii)

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:

Steps to draw a polygon.

The vertices of a polygon are usually labelled in alphabetical order and the polygon is named either clockwise or anticlockwise of the vertices.