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
#:#
#:#
#:#
#:#
of n sides, diagonals=?,diagonal from each vertex=#n#-3

we can see the series here

#2,5,9,14.........n#th #term#

#n#th 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#
#:#
#:#
#:#
#:##n#th 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