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How many diagonals does a regular 11-sided polygon contain? A. 35 B.
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25 Oct 2021, 05:36
25 Oct 2021, 05:36
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How many diagonals does a regular 11-sided polygon contain?
A. 35
B. 38
C. 40
D. 44
E. 55
A. 35
B. 38
C. 40
D. 44
E. 55
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Joined: 10 Apr 2015
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Re: How many diagonals does a regular 11-sided polygon contain? A. 35 B.
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25 Oct 2021, 06:10
25 Oct 2021, 06:10
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Carcass wrote:
How many diagonals does a regular 11-sided polygon contain?
A. 35
B. 38
C. 40
D. 44
E. 55
A. 35
B. 38
C. 40
D. 44
E. 55
A nice/fast approach that doesn't involve any counting techniques is to recognize that, for each of the 11 points (vertices), there are 8 possible points that we can connect to to create a diagonal.
ASIDE: there are 8 possible points because we cannot create a diagonal by connecting 2 adjacent points.
So, there are 8 possible diagonals for each of the 11 points
These means that there are 88 possible diagonals in total (8x11=88).
However, we need to recognize that this method counts each diagonal twice. For example, it counts the diagonal AB and the diagonal BA as 2 separate diagonals.
So, to account for this duplication, we'll divide 88 by 2 to get 44
Answer: D
Cheers,
Brent
Re: How many diagonals does a regular 11-sided polygon contain? A. 35 B.
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10 Sep 2023, 00:41
10 Sep 2023, 00:41
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