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

It is currently 27 Aug 2014, 19:32

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
User avatar
Joined: 19 Apr 2006
Posts: 231
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
Regular hexagon ABCDEF has a perimeter of 36. O is the [#permalink] New post 05 Aug 2006, 12:51
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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)? (see attached file)

a. 108-18pi
b. 54sqrt(3)-9pi
c. 54sqrt(3)-18pi
d. 108-27pi
e. 54sqrt(3)-27pi
Attachments

Hex.doc [72.5 KiB]
Downloaded 79 times

To download please login or register as a user

Intern
Intern
avatar
Joined: 11 Jul 2006
Posts: 4
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 09 Aug 2006, 12:41
E

hexagon:
if I don't know that the area of a regualr hexagon is (edge length)^2*(3/2)*sqrt(3)... (and why should I?)

...then I can figure it's made up of six equilateral triangles with sides of length 6.

by the pythagorean theorem, the height of each triangle is 3*sqrt(3)
(note each 60-60-60 triangle is 2 30-60-90 triangles and these have the old "one, two, radical three" ratio of sides we all loved in grade school, here the "two" is the length of the eqilateral triangle's side)

so the area is (1/2)*6*3*sqrt(3).

the area of the hexagon is then 6*(1/2)*6*3*sqrt(3) = 54*sqrt(3)


circles, all of radius 3, area 9pi:

the vertex angle of a regular hexagon is 120degrees.

so (120/360) or one third of each of six circles, plus the whole of the one circle in the middle of the hexagon, lies within the perimeter of the hexagon. three circles' area, all told.


inside the hexagon but outside the circle:

Ahex - 3*Acircle = 54*sqrt(3)- 3*9pi
Senior Manager
Senior Manager
User avatar
Joined: 05 Mar 2006
Posts: 348
Followers: 1

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

GMAT Tests User
 [#permalink] New post 09 Aug 2006, 12:50
Yup E.

6*9(sqrt3) - 9pi - 18pi

equals

54sqrt(3)-27pi
Director
Director
User avatar
Joined: 06 May 2006
Posts: 783
Followers: 3

Kudos [?]: 14 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Aug 2006, 12:52
E it is!

Area of Hexagon - 3*(Area of Circle of radius 3)
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2922
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 15

Kudos [?]: 79 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Aug 2006, 12:57
E

Area of circles A,B, C, D E and F that is inside the hexagon = 6*PI * 9/3 = 18 PI

Area of inner circle = 9 PI

Area of hexagon = 6 * 1/2 * 6 * SQRT(27) = 54 * SQRT(3)

Area of shaded region = 54 * SQRT(3) - 18PI - 9PI = 54 SQRT(3) - 27PI
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Manager
User avatar
Joined: 19 Apr 2006
Posts: 231
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Aug 2006, 15:46
sorry for the delay.... :oops:

but you are all winners!!!!!! :lol: Keep up the great work!!!!

E is the OA
SVP
SVP
avatar
Joined: 30 Mar 2006
Posts: 1741
Followers: 1

Kudos [?]: 25 [0], given: 0

GMAT Tests User
 [#permalink] New post 11 Aug 2006, 03:23
Side of hexagon = 6
Area of hexangons = 6*Sqr3/4 * 36 = 54sqr3 (Hexagon has 6 equilateral triangles)

Area of circle in the center = 9pi

Area of sector of the circle = 120/360 * 9pi = 3pi
Area of the six sectors = 6*3pi = 18pi

Area of shaded = 54sqr3 - (18pi+9Pi)
= 54sqr3 - 27pi
  [#permalink] 11 Aug 2006, 03:23
    Similar topics Author Replies Last post
Similar
Topics:
8 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
9 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
1 Regular hexagon ABCDEF has a perimeter of 36. O is the kizito2001 1 09 Dec 2007, 19:36
Regular hexagon ABCDEF has a perimeter of 36. O is the abhi_ferrari 3 26 Aug 2007, 19:42
Regular hexagon ABCDEF has a perimeter of 36. O is the ArvGMAT 1 27 Jun 2007, 20:01
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®.