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

 It is currently 23 Jan 2019, 04:14

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431
What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

### Show Tags

18 Jan 2018, 02:03
00:00

Difficulty:

25% (medium)

Question Stats:

87% (02:03) correct 13% (02:16) wrong based on 56 sessions

### HideShow timer Statistics

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 [ 6.24 KiB | Viewed 1620 times ]

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

### Show Tags

18 Jan 2018, 04:42
Bunuel wrote:

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

_________________

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
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4354
Location: India
GPA: 3.5
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

### Show Tags

18 Jan 2018, 06:26
Bunuel wrote:

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 [ 7.56 KiB | Viewed 1241 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
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)
Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD =  [#permalink]

### Show Tags

20 Jan 2018, 06:35
Bunuel wrote:

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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: What is the area of the trapezoid above if AB = BC = CD = 6, and AD = &nbs [#permalink] 20 Jan 2018, 06:35
Display posts from previous: Sort by