If a polygon has 24 sides, how many diagonals are there from each vertex? How many diagonals are there in all?

1 Answer
May 13, 2018

324 diagonals

Explanation:

if polygon is

of 4 sides, diagonals=2,diagonal from each vertex=1

of 5 sides, diagonals=5,diagonals from each vertex=2

of 6 sides, diagonals=9,diagonals from each vertex=3

of 7 sides, diagonals=14,diagonals from each vertex=4
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of n sides, diagonals=?,diagonal from each vertex=n-3

we can see the series here

2,5,9,14.........nth term

nth term can be found as

1st term=2=(1^2+3(1))/2

2nd term=5=(2^2+3(2))/2

3rd term=9=(3^2+3(3))/2
:
:
:
:nth term=(n^2+3n)/2

(there's a kinda shortcut for that if u'r interested ,contact me on my email)

for polygon with 24 sides put n=24

no. of diagonals are=(24^2+3(24))/2 = 324 ,number of diagonals from each vertex=21