Question

find the number of diagonals of nonagon​

Answer 1

Answer:

The formula for determining the number of diagonals of an n-sided polygon is n(n - 3)/2; thus, a nonagon has 9(9 - 3)/2 = 9(6)/2 = 54/2 = 27 diagonals. The diagonal of a polygon is any line segment joining two nonadjacent vertices.

Answer 2

The number of diagonals of a nonagon = 27

Given :

A nonagon

To find :

The number of diagonals of a nonagon

Formula :

The number of diagonals of an n sided polygon is n(n - 3)/2

Solution :

Step 1 of 2 :

Write down the number of sides

Here the given polygon is nonagon

The number of sides in a nonagon = n = 9

Step 2 of 2 :

Calculate the number of diagonals

We know that the number of diagonals of an n sided polygon is n(n - 3)/2

Since number of sides in a nonagon = n = 9

Hence the number of diagonals of a nonagon

$\displaystyle \sf{ = \frac{9 \times (9 - 3)}{2} }$

$\displaystyle \sf{ = \frac{9 \times 6}{2} }$

$\displaystyle \sf{ = \frac{54}{2} }$

$\displaystyle \sf{ = 27 }$

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