Question

Find the maximum number of diagonals that can be drawn in n-sided polygon. Also, find number of diagonals if
(a) n = 12 sides.
(b) n = 15 sides
(c) Decagon

Answer 1

use the formula n (n-3)/2 n stands for number of sides

Answer 2

Answer:

(a) Number of diagonals = 54

(b) Number of diagonals = 90

(c) Number of diagonals = 35

Step-by-step explanation:

We know that the Maximum number of diagonals drawn in an 'n-sided polygon' is given by,

$Number\ of\ diagonals=\frac{n(n-3)}{2}$

Here,

n = Number of sides of the polygon

Now,

(a) n = 12

The number of diagonals in the polygon having n = 12 sides is given by,

$D=\frac{12(12-3)}{2}=54$

Here,

D is the number of Diagonals.

(b) n = 15

The number of diagonals in the polygon having n = 15 sides is given by,

$D=\frac{15(15-3)}{2}=90$

(c) Decagon

In a Decagon the number of sides, n = 10

The number of diagonals in the polygon having n = 10 sides is given by,

$D=\frac{10(10-3)}{2}=35$