GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Oct 2019, 12:44

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.

Close

Request Expert Reply

Confirm Cancel

What is the area of the trapezoid above if AB = BC = CD = 6, and AD =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

Show Tags

New post 18 Jan 2018, 03:03
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

88% (02:03) correct 12% (02:24) wrong based on 61 sessions

HideShow timer Statistics

CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

Show Tags

New post 18 Jan 2018, 05:42
Bunuel wrote:
Image
What is the area of the trapezoid above if AB = BC = CD = 6, and AD = 12?

A. \(6\sqrt{6}\)

B. \(18\sqrt{2}\)

C. \(18\sqrt{3}\)

D. \(27\sqrt{2}\)

E. \(27\sqrt{3}\)


Attachment:
2018-01-18_1400.png


Area of Trapezium = SUm of the two parallel sides * Distance between parallel sides / 2

i.e. Area of Trapezium = = (BC+AD)*Distance /2

Distance between two sides = Perpendicular dropped from B on AD = h

The triangle will have side 3-6-h

Now using pythagorus theorem, h = 3√3

Hence Area of Trapezium = (6+12)*3√3 /2 = 27√3

Answer: option E
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4772
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

Show Tags

New post 18 Jan 2018, 07:26
Bunuel wrote:
Image
What is the area of the trapezoid above if AB = BC = CD = 6, and AD = 12?

A. \(6\sqrt{6}\)

B. \(18\sqrt{2}\)

C. \(18\sqrt{3}\)

D. \(27\sqrt{2}\)

E. \(27\sqrt{3}\)


Attachment:
The attachment 2018-01-18_1400.png is no longer available
Attachment:
2018-01-18_1400.png
2018-01-18_1400.png [ 7.56 KiB | Viewed 1917 times ]


Here BE = CF =\(3\sqrt{3}\)

Area of Triangle ABE + Triangle CFD = \(2*\frac{1}{2}*3*3\sqrt{3}\) = \(9\sqrt{3}\)

Area of rectangle BEFC = \(6*3\sqrt{3}\) = \(18\sqrt{3}\)

So, The total area is \(27\sqrt{3}\), answer will be (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8104
Location: United States (CA)
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

Show Tags

New post 20 Jan 2018, 07:35
Bunuel wrote:
Image
What is the area of the trapezoid above if AB = BC = CD = 6, and AD = 12?

A. \(6\sqrt{6}\)

B. \(18\sqrt{2}\)

C. \(18\sqrt{3}\)

D. \(27\sqrt{2}\)

E. \(27\sqrt{3}\)


Attachment:
2018-01-18_1400.png


Notice that trapezoid ABCD is an isosceles trapezoid since AB = CD. By dropping a perpendicular from B to AD and C to AD we have created two right triangles and a rectangle in the middle. Let E and F be points on AD where the perpendiculars are dropped from B and C, respectively. We see that AE = FD and BE = CF. We can let n = AE = FD and h = BE = CF.

Since BC = EF, we can say that:

EF + n + n = AD

6 + 2n = 12

2n = 6

n = 3 = AE

Since AE^2 + BE^2 = AB^2, we have

3^2 + h^2 = 6^2

h^2 = 27

h = 3√3

We now can determine the area of the trapezoid.

area = (base 1 + base 2)/2 x height

area = (6 + 12)/2 x 3√3 = 9 x 3√3 = 27√3

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =   [#permalink] 20 Jan 2018, 07:35
Display posts from previous: Sort by

What is the area of the trapezoid above if AB = BC = CD = 6, and AD =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne