Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Sep 2014, 13:58

Close

GMAT 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

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Regular hexagon ABCDEF has a perimeter of 36. O is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 07 Feb 2007
Posts: 54
Location: Philadelphia
Followers: 1

Kudos [?]: 0 [0], given: 0

Regular hexagon ABCDEF has a perimeter of 36. O is the [#permalink] New post 26 Aug 2007, 19:42
Regular hexagon ABCDEF has a perimeter of 36. O is the center of the hexagon and of circle O. Circles A, B, C, D, E, and F have centers at A, B, C, D, E, and F, respectively. If each circle is tangent to the two circles adjacent to it and to circle O, what is the area of the shaded region (inside the hexagon but outside the circles)?


108 – 18*pi
54*sqrt3 - 9*pi
54*sqrt3 - 18*pi
108 - 27*pi
54*sqrt3 - 27*pi

Pls see attachment for the figure
Attachments

doc.doc [72.5 KiB]
Downloaded 31 times

To download please login or register as a user

Senior Manager
Senior Manager
avatar
Joined: 27 Jul 2006
Posts: 299
Followers: 1

Kudos [?]: 7 [0], given: 0

 [#permalink] New post 26 Aug 2007, 20:06
I ger 54 square root 3 minus 27pi

here is how i did it.

Six sides six inches each the area of which will be six equilateral triangles with a hight of 3 sqare root of 3 we have six circles with an area of 9pi each circle takes away an area that is eqaul to 120 degrees of the circle.

{(120/360)54pi} is the area taken away by the outside circles plus the 9pi by the inner circle

subtract the area of the hex from this and you get what is above.
Manager
Manager
avatar
Joined: 03 Sep 2006
Posts: 233
Followers: 1

Kudos [?]: 5 [0], given: 0

 [#permalink] New post 26 Aug 2007, 20:20
I got 54 sqrt 3 - 27*Pi:

1) hexagon consists of 6 equilateral with the side 6, so the area of hexagon:
S1 = 6 * 1/2 * (3 sqrt 3) * 6 = 54 sqrt 3

2) the area of 6 parts of a square =
S2 = 6 * ((Pi * 9) / 3) = 18*Pi

S = S1 - S2 = 54 sqrt 3 - 18*Pi -9*Pi (area of the 7th circle)

Last edited by Whatever on 28 Aug 2007, 00:45, edited 1 time in total.
Manager
Manager
avatar
Joined: 07 Feb 2007
Posts: 54
Location: Philadelphia
Followers: 1

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 27 Aug 2007, 06:16
defenestrate wrote:
I ger 54 square root 3 minus 27pi

here is how i did it.

Six sides six inches each the area of which will be six equilateral triangles with a hight of 3 sqare root of 3 we have six circles with an area of 9pi each circle takes away an area that is eqaul to 120 degrees of the circle.

{(120/360)54pi} is the area taken away by the outside circles plus the 9pi by the inner circle

subtract the area of the hex from this and you get what is above.


Thanks! OA is E. I was missing the area included {(120/360)54pi}.
  [#permalink] 27 Aug 2007, 06:16
    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic A regular hexagon has a perimeter of 30 units. What is the gmihir 6 30 Apr 2012, 00:02
10 Experts publish their posts in the topic Regular hexagon ABCDEF has a perimeter of 36. O is the cente gmatjon 18 22 Jan 2010, 10:10
4 Experts publish their posts in the topic Regular hexagon ABCDEF has a perimeter of 36. O is the center of the kizito2001 4 09 Dec 2007, 19:36
Regular hexagon ABCDEF has a perimeter of 36. O is the ArvGMAT 1 27 Jun 2007, 20:01
Regular hexagon ABCDEF has a perimeter of 36. O is the acfuture 6 05 Aug 2006, 12:51
Display posts from previous: Sort by

Regular hexagon ABCDEF has a perimeter of 36. O is the

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.