Question

HOW MANY DIAGONALS CAN BE DRAWN IN A polygon
WITH 9 SIDES.​

Answer 1

Answer:

27

Step-by-step explanation:

So, number of diagonals=9C2–9

For any polygon with n sides, total number of diagonals possible= nC2-n, which can be simplified further to (n*(n-3))/2. Thus, total diagonals=9*6/2 = 27.

hope it helps you.....

Answer 2

There are 27 diagonals of the polygon with 9 sides.

Tips:

If there are $n$ diagonals in a polygon, then there are $d=\dfrac{n(n-3)}{2}$ diagonals.

Step-by-step explanation:

Given, there are 9 sides of the polygon.

Then n = 9

Now, put n = 9 in the formula $d=\dfrac{n(n-3)}{2}$, we get

$\quad d=\dfrac{9(9-3)}{2}$

$\Rightarrow d=\dfrac{9\times 6}{2}$

⇒ d = 9 × 3

⇒ d = 27

Therefore, there are 27 diagonals of the polygon with 9 sides.