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How many diagonals does a regular 20-sided polygon have?
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26 Oct 2017, 23:40
26 Oct 2017, 23:40
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88% (00:42) correct
11% (01:03) wrong based on 18 sessions
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How many diagonals does a regular 20-sided polygon have?
(A) 60
(B) 120
(C) 170
(D) 240
(E) 400
Kudos for correct solution.
(A) 60
(B) 120
(C) 170
(D) 240
(E) 400
Kudos for correct solution.
Re: How many diagonals does a regular 20-sided polygon have?
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27 Oct 2017, 02:41
27 Oct 2017, 02:41
3
We can start by computing the number of ways two points can be chosen from 20 vertices., i.e. \(20C2 = \frac{20!}{18!2!} = 190\).
Then, we have to notice that with this method we have included not only diagonals but also sides of the polygon because sides join vertices too. Thus, we have to subtract 20 sides from 190 and we get our answer 170. Answer C
Then, we have to notice that with this method we have included not only diagonals but also sides of the polygon because sides join vertices too. Thus, we have to subtract 20 sides from 190 and we get our answer 170. Answer C
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Re: How many diagonals does a regular 20-sided polygon have?
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27 Oct 2017, 10:37
27 Oct 2017, 10:37
2
To solve this problem in the exam, better if we learn this formula for calculating the number of diagonals in a regular polygon i.e.
N(N-3)/2 where N is the no. of sides.
Lets take our problem, we are provided 20 sides.Therefore,
N(N-3)/2 = 20(20-3)/2 = 170.
N(N-3)/2 where N is the no. of sides.
Lets take our problem, we are provided 20 sides.Therefore,
N(N-3)/2 = 20(20-3)/2 = 170.
