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How many diagonals are in a figure enclosed into the regular polygon

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motion2020
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How many diagonals are in a figure enclosed into the regular polygon [#permalink] New post   21 Sep 2021, 01:55
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How many diagonals are in a figure enclosed into the regular polygon with 26 sides, if the area of this enclosed figure is equal to exactly half of the area of the original regular polygon?

(A) 66
(B) 77
(C) 88
(D) 99
(E) 111
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eskay1981
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Re: How many diagonals are in a figure enclosed into the regular polygon [#permalink] New post   22 Sep 2021, 14:16
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motion2020 wrote:
How many diagonals are in a figure enclosed into the regular polygon with 26 sides, if the area of this enclosed figure is equal to exactly half of the area of the original regular polygon?

(A) 66
(B) 77
(C) 88
(D) 99
(E) 111


The formula for number of diagonals in a polygon = n(n−3)2
Here the 26 sided polygon is cut into two halves, so the number of sides in one of the half = 262+1
So answer is 14∗112=77
Answer is B) 77
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How many diagonals are in a figure enclosed into the regular polygon [#permalink] New post   22 Sep 2021, 19:35
I am not a big fan of formulas. So, yes area enclosed is the figure having 26/2+1=14 sides that provide 14 points. The number of possible diagonal side arrangements between any 2 points is 14C2 and less 14 sides of the enclosed figure itself.

14C2-14 = 14*13/2-14 = 77

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Re: How many diagonals are in a figure enclosed into the regular polygon [#permalink] New post   26 Sep 2022, 02:49
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