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how many internal diagonals does a decagon (ten sided polygon) have?

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how many internal diagonals does a decagon (ten sided polygon) have?  [#permalink]

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New post 27 Feb 2015, 03:18
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:12) correct 35% (01:43) wrong based on 166 sessions

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how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25
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Joined: 02 Aug 2009
Posts: 8023
Re: how many internal diagonals does a decagon (ten sided polygon) have?  [#permalink]

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New post 27 Feb 2015, 03:30
2
1
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35
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Re: how many internal diagonals does a decagon (ten sided polygon) have?  [#permalink]

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New post 28 Feb 2015, 03:20
1
1
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 10
No. of diagonals = 10(10 - 3)/2
= 35
Hence option 4.

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Re: how many internal diagonals does a decagon (ten sided polygon) have?  [#permalink]

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New post 03 Jan 2019, 09:06
1
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


Well I took a different approach:

Square with 4 sides = 2 diagonals
Pentagon 5 sides = 5 diagonals (increase of 3)
Hexagon 6 sides = 9 diagonals (increase of 4)
Septagon 7 side = 14 diagons (increase of 5 from previous)

Hence the diagonals are increasing in a certain orders and their difference increase is a normal AP: 3, 4, 5....so on
Hence for 8 sides = 20
9 sides = 27
10 sides = 35 diagonals

Hence the answer is D
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Re: how many internal diagonals does a decagon (ten sided polygon) have?   [#permalink] 03 Jan 2019, 09:06
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