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The diagonal of a polygon is a line segment from any vertex
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01 Dec 2018, 10:58
01 Dec 2018, 10:58
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Question Stats:
63% (00:56) correct
36% (00:56) wrong based on 66 sessions
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The diagonal of a polygon is a line segment from any vertex to any non-adjacent vertex. The diagram below shows a regular decagon, a 10-sided polygon, with two diagonals drawn. How many possible diagonals does the regular decagon have?
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg [ 11.86 KiB | Viewed 18151 times ]
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GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg [ 11.86 KiB | Viewed 18151 times ]
Show: :: OA
35
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Re: The diagonal of a polygon is a line segment from any vertex
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03 Dec 2018, 11:11
03 Dec 2018, 11:11
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Carcass wrote:
The diagonal of a polygon is a line segment from any vertex to any non-adjacent vertex. The diagram below shows a regular decagon, a 10-sided polygon, with two diagonals drawn. How many possible diagonals does the regular decagon have?
Attachment:
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg
Show: :: OA
35
A polygon with 10 sides will also have 10 vertices,
Each individual vertex can have 7 diagonals. Here's why:
First, the vertex cannot create a diagonal when connected to itself.
Second, the vertex cannot create a diagonal with the two points on either side of it, since that line will not be a diagonal.
So, in a polygon with 10 vertices, each vertex will have 7 diagonals connected to it.
So, the total number of diagonals = (10)(7) = 70
IMPORTANT: Did you see that we counted every diagonal TWICE?
For example, if the line joining vertex A and vertex F is a diagonal, we count that diagonal once when counting the 7 diagonals at vertex A, AND we count that diagonal once when counting the 7 diagonals at vertex F.
To account for this duplication, we'll divide the number of diagonal by 2.
So, the TOTAL number of diagonals = 70/2 = 35
Answer: 35
Cheers,
Brent
Re: The diagonal of a polygon is a line segment from any vertex
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13 Jan 2019, 01:52
13 Jan 2019, 01:52
3
Expert Reply
Theres a formula for this,
n*(n-3)/2
10*(10-3)/2 = 35
n*(n-3)/2
10*(10-3)/2 = 35
