Question

How many diagonals does a regular hexagon have?
$$\begin{gathered} \left(a\right)8 \\ \left(b\right)9 \\ \left(c\right)10 \\ \left(d\right)11 \end{gathered}$$

Answer 1

Hint:In this question, we use the relation between the number of diagonals with the number of sides of a polygon. The number of diagonals of an n sided polygon is given by $D_n={\displaystyle \frac{n\left(n-3\right)}{2}}$ .

Complete step-by-step answer:
Given, we have a regular hexagon. A regular hexagon is a polygon with six equal sides and angles.
So, the number of sides in a regular hexagon is 6.
Now, using the relation between the number of diagonals and number of sides .
$\Rightarrow D_n={\displaystyle \frac{n\left(n-3\right)}{2}}$ , where $D_n$ is a number of diagonals.
For regular hexagon values of n=6.
$$\begin{gathered} \Rightarrow D_n={\displaystyle \frac{6\left(6-3\right)}{2}} \\ \Rightarrow D_n={\displaystyle \frac{6\times 3}{2}} \\ \Rightarrow D_n={\displaystyle \frac{18}{2}} \\ \Rightarrow D_n=9 \end{gathered}$$
Therefore, in a regular hexagon the number of diagonals is 9.
So, the correct option is (b).

Note: Whenever we face such types of problems we use some important points. First we find the number of sides in a regular polygon (in regular hexagon n=6) then use the formula of the number of diagonals with numbers of sides of the polygon. So, after calculation we will get the required answer.