## 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,

• 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}

 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:

• 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.

## 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,

• 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}

 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:

• 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.