Question

The number of diagonals in an octagon is
$
  \left( a \right)8 \\
  \left( b \right)40 \\
  \left( c \right)20 \\
  \left( d \right)32 \\
$

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 octagon. A regular octagon is a polygon with eight equal sides and angles.
So, the number of sides in a regular octagon is 8.
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 octagon value of n=8.
$
   \Rightarrow {D_n} = \dfrac{{8\left( {8 - 3} \right)}}{2} \\
   \Rightarrow {D_n} = \dfrac{{8 \times 5}}{2} \\
   \Rightarrow {D_n} = \dfrac{{40}}{2} \\
   \Rightarrow {D_n} = 20 \\
$
Therefore, in a regular octagon the number of diagonals is 20.
So, the correct option is (c).
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 octagon n=8) 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.