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# In a polygon with 9 equal sides and 9 equal angles

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Intern
Joined: 25 Mar 2013
Posts: 3
Location: Italy
WE: General Management (Other)
In a polygon with 9 equal sides and 9 equal angles  [#permalink]

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02 Apr 2013, 09:25
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00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:08) correct 46% (01:19) wrong based on 170 sessions

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In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

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Labor omnia vincit

Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: In a polygon with 9 equal sides and 9 equal angles  [#permalink]

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02 Apr 2013, 09:31
2
3
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

The # of diagonals in $$n$$ sided polygon equals to $$C^2_n-n=\frac{n(n-3)}{2}$$: $$C^2_n$$ choose any two vertices out of $$n$$ points to connect minus $$n$$ sides, which won't be diagonals.

So, # of diagonals in 9 sided polygon is $$\frac{n(n-3)}{2}=27$$.

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Joined: 14 Jun 2012
Posts: 28
Concentration: Strategy, Technology
Schools: Goizueta '15 (D)
GMAT 1: 640 Q47 V32
GMAT 2: 640 Q47 V32
GMAT 3: 730 Q49 V40
WE: Information Technology (Computer Software)
Re: In a polygon with 9 equal sides and 9 equal angles  [#permalink]

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02 Apr 2013, 09:36
3
4
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

To find the number of diagonals in a polygon with n sides, use the following formula:
n (n-3) / 2.

9*6/2 = 27.

Here’s where the diagonal formula comes from and why it works. Each diagonal connects one point to another point in the polygon that isn’t its next-door neighbor. In an n-sided polygon, you have n starting points for diagonals. And each diagonal can go to (n – 3) ending points because a diagonal can’t end at its own starting point or at either of the two neighboring points. So the first step is to multiply n by (n – 3). Then, because each diagonal’s ending point can be used as a starting point as well, the product n(n – 3) counts each diagonal twice. That’s why you divide by 2.

http://www.dummies.com/how-to/content/h ... lygon.html
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: In a polygon with 9 equal sides and 9 equal angles  [#permalink]

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02 Apr 2013, 09:33
1
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

Similar question to practice: how-many-diagonals-does-a-polygon-with-21-sides-have-if-one-101540.html

Hope it helps
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Joined: 09 Sep 2013
Posts: 9138
Re: In a polygon with 9 equal sides and 9 equal angles  [#permalink]

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16 Nov 2018, 18:13
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Re: In a polygon with 9 equal sides and 9 equal angles &nbs [#permalink] 16 Nov 2018, 18:13
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# In a polygon with 9 equal sides and 9 equal angles

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