GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The diagonal of a polygon is a line segment from any vertex
[#permalink]
01 Dec 2018, 10:58
01 Dec 2018, 10:58
Expert Reply
00:00
Question Stats:
62% (00:56) correct
37% (00:56) wrong based on 67 sessions
Hide Show timer Statistics
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 19187 times ]
Attachment:
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg [ 11.86 KiB | Viewed 19187 times ]
Show: :: OA
35
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The diagonal of a polygon is a line segment from any vertex
[#permalink]
03 Dec 2018, 11:11
03 Dec 2018, 11:11
1
1
Bookmarks
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
[#permalink]
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
