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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Hexagon sum of lengths of diagonals [#permalink]
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.

Re: A regular hexagon has a perimeter of 30 units. What is the [#permalink]
30 Apr 2012, 02:23

7

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

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 4864 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 \(3*10+6*5\sqrt{3}=30(1+\sqrt{3})\).

Re: A regular hexagon has a perimeter of 30 units. What is the [#permalink]
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).

Re: A regular hexagon has a perimeter of 30 units. What is the [#permalink]
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 ?

Re: A regular hexagon has a perimeter of 30 units. What is the [#permalink]
28 Apr 2015, 04:48

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. _________________

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...