December 17, 2018 December 17, 2018 06:00 PM PST 07:00 PM PST Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong. December 17, 2018 December 17, 2018 10:00 PM PST 11:00 PM PST From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Mar 2012
Posts: 38

A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
30 Apr 2012, 00:02
Question Stats:
86% (00:17) correct 14% (00:00) wrong based on 19 sessions
HideShow timer Statistics
A regular hexagon has a perimeter of 30 units. What is the sum of the lenghts of all its diagonals ?
Sorry, I can't recall the answer choices but am sure answer 30 is incorrect one.




Math Expert
Joined: 02 Sep 2009
Posts: 51239

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
30 Apr 2012, 02:23
gmihir wrote: A regular hexagon has a perimeter of 30 units. What is the sum of the lenghts of all its diagonals ?
Sorry, I can't recall the answer choices but am sure answer 30 is incorrect one. Look at the diagram below: Attachment:
Hexagon.png [ 17.48 KiB  Viewed 13341 times ]
There are 9 diagonals in a hexagon. Each of 3 red diagonals equal to \(2*side=2*5=10\) (since regular hexagon is made of 6 equilateral triangles); Each of 6 blue diagonals equal to \(2*(side*\frac{\sqrt{3}}{2})=5\sqrt{3}\) (notice that in 30°, 60°, 90° triangle, where the sides are always in the ratio \(1 : \sqrt{3}: 2\), half of the blue diagonal is the leg opposite 60°, so it equals to \(side*\frac{\sqrt{3}}{2}\)); So, the sum of the lenghts of all diagonals is \(3*10+6*5\sqrt{3}=30(1+\sqrt{3})\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 27 Oct 2011
Posts: 12

Re: Hexagon sum of lengths of diagonals
[#permalink]
Show Tags
30 Apr 2012, 00:27
In a regular hexagon length of each diagonal is twice of each side.Since there are 3 diagonals and 6 sides, sum of lengths of diagonals will be equal to perimeter of hexagon.You can think a hexagon as six equilateral triangles joined together. Hope it helps.. Answer is 30.



Intern
Joined: 01 Mar 2012
Posts: 21
Concentration: Operations, Finance
GPA: 3.3
WE: Engineering (Manufacturing)

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
03 May 2012, 20:53
Another good example of Deception, Excellent question and excellent explanation by bunuel. The ratio of the sides are deduced from the SINE FORMULA ie (a/sinA)=(b/sinB)=(c/sinC).



Intern
Status: Waiting
Joined: 11 Dec 2012
Posts: 49
Location: Bahrain
Concentration: Healthcare, General Management
GMAT 1: 640 Q49 V24 GMAT 2: 720 Q49 V40
WE: Sales (Other)

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
29 Jun 2013, 21:44
Bunuel wrote: Each of 6 blue diagonals equal to \(2*(side*\frac{\sqrt{3}}{2})=5\sqrt{3}\) (notice that in 30°, 60°, 90° triangle, where the sides are always in the ratio \(1 : \sqrt{3}: 2\), half of the blue diagonal is the leg opposite 60°, so it equals to \(side*\frac{\sqrt{3}}{2}\));
Bunuel: Can you please explain the above mentioned step in detail. How did you calculate the 90 degree angle or the small 30 degree angle ? Thank you



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
16 Oct 2013, 01:58
Formula for no. of diagonals in a N sided polygon = n(n3)  2
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 07 Jan 2013
Posts: 20
Location: Poland
GPA: 3.8

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
26 Dec 2013, 11:24
I think the right answer should be 30(1+2 squareroot3)



Manager
Joined: 19 Aug 2016
Posts: 150
Location: India
GPA: 3.82

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
20 Apr 2017, 04:51
PareshGmat wrote: Formula for no. of diagonals in a N sided polygon =
n(n3)  2 Just to clarify: you mean n(n3) divided by 2 right?
_________________
Consider giving me Kudos if you find my posts useful, challenging and helpful!



Manager
Joined: 11 Feb 2017
Posts: 189

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
21 Apr 2017, 08:44
I have a answer but can someone find any flaw in it? Becoz Im not sure if its right or not...
S= side of hexagon D = diagonal of a regular hexagon
6*S = 30
S=5 ;
Property: The diagonal of a regular hexagon, is twice the side length.
D = 2*S D = 10;
Regular hexagon has 6 diagonals
6*D is sum of all diagonals
60 Answer



Manager
Joined: 11 Feb 2017
Posts: 189

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
21 Apr 2017, 08:45
Bunuel wrote: gmihir wrote: A regular hexagon has a perimeter of 30 units. What is the sum of the lenghts of all its diagonals ?
Sorry, I can't recall the answer choices but am sure answer 30 is incorrect one. Look at the diagram below: Attachment: Hexagon.png There are 9 diagonals in a hexagon. Each of 3 red diagonals equal to \(2*side=2*5=10\) (since regular hexagon is made of 6 equilateral triangles); Each of 6 blue diagonals equal to \(2*(side*\frac{\sqrt{3}}{2})=5\sqrt{3}\) (notice that in 30°, 60°, 90° triangle, where the sides are always in the ratio \(1 : \sqrt{3}: 2\), half of the blue diagonal is the leg opposite 60°, so it equals to \(side*\frac{\sqrt{3}}{2}\)); So, the sum of the lenghts of all diagonals is \(3*10+6*5\sqrt{3}=30(1+\sqrt{3})\). Hope it's clear. I have a answer but can someone find any flaw in it? Becoz Im not sure if its right or not... S= side of hexagon D = diagonal of a regular hexagon 6*S = 30 S=5 ; Property: The diagonal of a regular hexagon, is twice the side length. D = 2*S D = 10; Regular hexagon has 6 diagonals 6*D is sum of all diagonals 60 Answer



NonHuman User
Joined: 09 Sep 2013
Posts: 9195

Re: A regular hexagon has a perimeter of 30 units. What is the
[#permalink]
Show Tags
27 Nov 2018, 23:05
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A regular hexagon has a perimeter of 30 units. What is the &nbs
[#permalink]
27 Nov 2018, 23:05






