Hi! I have a doubt on heptagons,octagon, nonagon& decagon. How many diagonals do they have? How to draw them?

Answer :

We can use formula to find number of distinct diagonals .

Number of diagonals  of n - sided polygon  = $\frac{n \left( n - 3 \right)}{2}$

So,

Number of diagonals of heptagon (  We know in heptagon we have 7 sides , So n  =   7 )   =  $\frac{7 \left( 7 - 3 \right)}{2} = \frac{7 \times 4}{2} = 7 \times 2$  =  14  
And

Number of diagonals of octagon (  We know in octagon we have 8 sides , So n  =  8 )   =  $\frac{8 \left(8 - 3 \right)}{2} = \frac{8 \times 5}{2} = 4 \times 5$  =  20
And

Number of diagonals of nonagon (  We know in nonagon we have 9 sides , So n  = 9 )   =  $\frac{9 \left(9 - 3 \right)}{2} = \frac{9 \times 6}{2} = 9 \times 3$  =  27
And

Number of diagonals of decagon (  We know in decagon we have 10 sides , So n  =  10 )   =  $\frac{10 \left(10 - 3 \right)}{2} = \frac{10 \times 7}{2} = 5 \times 7$  =  35
And

We can draw these diagonals by joining each non consecutive vertices.

Here we have draw diagonals of heptagon , As :

You can try to draw diagonals  for different polygon by yourself and if still have any doubt , Kindly get back to us so we can help you precisely  .