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

 It is currently 17 Nov 2018, 09:25

# Join here

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

# Equilateral triangle AED lies inside square ABCD, as shown above. If

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50623
Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

20 Oct 2016, 23:15
00:00

Difficulty:

25% (medium)

Question Stats:

84% (01:30) correct 16% (01:59) wrong based on 86 sessions

### HideShow timer Statistics

Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. $$19-9\sqrt{3}$$

B. $$36-18\sqrt{3}$$

C. $$9\sqrt{3}$$

D. $$3(12-3\sqrt{3})$$

E. $$2(9+3\sqrt{3})$$

Attachment:

T7902.png [ 7.59 KiB | Viewed 2481 times ]

_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4219
Location: India
GPA: 3.5
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

21 Oct 2016, 12:02
1
Bunuel wrote:

Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. $$19-9\sqrt{3}$$

B. $$36-18\sqrt{3}$$

C. $$9\sqrt{3}$$

D. $$3(12-3\sqrt{3})$$

E. $$2(9+3\sqrt{3})$$

Attachment:
T7902.png

Area of shaded region = Area of Square - Area of the Equilateral Triangle

Area of the square $$= 6^2 = 36$$

Area of the Equilateral Triangle =$$\frac{√3}{4}*6^2$$ = $$9√3$$

So, Area of shaded region = $$36$$ $$-$$ $$9√3$$

Or, Area of shaded region = $$3(12-3\sqrt{3})$$

_________________

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 )

Intern
Joined: 18 Sep 2016
Posts: 49
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

21 Oct 2016, 12:36
Bunuel wrote:

Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. $$19-9\sqrt{3}$$

B. $$36-18\sqrt{3}$$

C. $$9\sqrt{3}$$

D. $$3(12-3\sqrt{3})$$

E. $$2(9+3\sqrt{3})$$

Attachment:
T7902.png

the side of the equilateral triangle is 6 as theside of the square.

the height of an equilateral triangle is equal to $$\frac{side}{2}*\sqrt{3}$$ = $$3\sqrt{3}$$

the area of the triangle is $$\frac{1}{2}*6*3*\sqrt{3}$$ = $$9\sqrt{3}$$

the area of the square is $$6*6 = 36$$

the difference between the area of the square and the area of the triangle is $$36-$$$$9\sqrt{3}$$ $$= 3*(12+3\sqrt{3})$$

_________________

Please press Kudos if you like my post

SVP
Joined: 06 Nov 2014
Posts: 1882
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

21 Oct 2016, 17:48
Bunuel wrote:

Equilateral triangle AED lies inside square ABCD, as shown above. If the side of the square is 6, what is the area of the shaded region?

A. $$19-9\sqrt{3}$$

B. $$36-18\sqrt{3}$$

C. $$9\sqrt{3}$$

D. $$3(12-3\sqrt{3})$$

E. $$2(9+3\sqrt{3})$$

Attachment:
T7902.png

Area of the square = 6*6 = 36
Since the triangle is an equilateral triangle and shares one side with the square, side of the triangle = 6

Area of the triangle = (√3/4)*6^2 = 9√3

Area of the shaded region = 36 - 9√3 = 3(12 - 3√3)

Correct Option: D
Manager
Joined: 11 Jul 2016
Posts: 80
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

22 Oct 2016, 03:55
This seems to be formula based

Area of square = a ^2 = 36

Area of equilateral triangle = Sq rt 3/4 * a^2
= 9 * sq rt 3

Area of shaded region = 36 - 9*sq rt 3
= 3(12−3√3)

Option D

Non-Human User
Joined: 09 Sep 2013
Posts: 8801
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If  [#permalink]

### Show Tags

08 Jul 2018, 22:12
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.
_________________
Re: Equilateral triangle AED lies inside square ABCD, as shown above. If &nbs [#permalink] 08 Jul 2018, 22:12
Display posts from previous: Sort by