Question

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

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 ${D_n} = \dfrac{{n\left( {n - 3} \right)}}{2}$ .

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 .
$\Rightarrow {D_n} = \dfrac{{n\left( {n - 3} \right)}}{2}$ , where ${D_n}$ is a number of diagonals.
For regular hexagon values of n=6.
$\Rightarrow {D_n} = \dfrac{{6\left( {6 - 3} \right)}}{2} \\\ \Rightarrow {D_n} = \dfrac{{6 \times 3}}{2} \\\ \Rightarrow {D_n} = \dfrac{{18}}{2} \\\ \Rightarrow {D_n} = 9 \\\$
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.