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

 It is currently 22 Feb 2019, 10:33

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# Find the area of AEDC, if ABCDEF is a regular hexagon with each side b

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

31 May 2017, 23:30
5
00:00

Difficulty:

85% (hard)

Question Stats:

54% (02:57) correct 46% (03:00) wrong based on 65 sessions

### HideShow timer Statistics

Find the area of AEDC, if ABCDEF is a regular hexagon with each side being equal to “a” units.

A. $$\frac{√3a^2}{4}$$
B. $$\frac{3√3a^2}{4}$$
C. $$√3a^2$$
D. $$\frac{5√3a^2}{4}$$
E. $$\frac{7√3a^2}{4}$$
Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1366
Location: Viet Nam
Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

01 Jun 2017, 00:16
niteshwaghray wrote:
Find the area of AEDC, if ABCDEF is a regular hexagon with each side being equal to “a” units.

A. $$\frac{√3a^2}{4}$$
B. $$\frac{3√3a^2}{4}$$
C. $$√3a^2$$
D. $$\frac{5√3a^2}{4}$$
E. $$\frac{7√3a^2}{4}$$

Attachment:

mugeYL1.png [ 10.08 KiB | Viewed 6195 times ]

Each angle of ABCDEF is 120 degree.

O is the center of triangle ACE. We have $$\widehat{AOE} =\widehat{COE} = \widehat{AOC} = 120^o$$

We could easily have $$\Delta AFE = \Delta EDC = \Delta CBA = \Delta AOC = \Delta COE = \Delta EOA$$
Hence $$S_{ AFE} = S_{ EDC} = S_{ CBA} = S_{AOC} = S_{COE} = S_{EOA}$$

OD cuts EC at M. Triangle OCD is an equilateral triangle. Hence $$S_{OCD}=\frac{1}{2} \times a \times \frac{a\sqrt{3}}{2}=\frac{a^2\sqrt{3}}{4}$$

Hence $$S_{OEDC}=2S_{OCD}=2 \times \frac{a^2\sqrt{3}}{4} = \frac{a^2\sqrt{3}}{2}$$
So $$S_{OEC}=\frac{1}{2} S_{OEDC} =\frac{1}{2} \times \frac{a^2\sqrt{3}}{2} = \frac{a^2\sqrt{3}}{4}$$

$$S_{AEDC}=4S_{OEC}=4 \times \frac{a^2\sqrt{3}}{4}=a^2\sqrt{3}$$

_________________
Intern
Joined: 15 Jun 2013
Posts: 46
Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

01 Jun 2017, 08:01
nguyendinhtuong wrote:
niteshwaghray wrote:
Find the area of AEDC, if ABCDEF is a regular hexagon with each side being equal to “a” units.

A. $$\frac{√3a^2}{4}$$
B. $$\frac{3√3a^2}{4}$$
C. $$√3a^2$$
D. $$\frac{5√3a^2}{4}$$
E. $$\frac{7√3a^2}{4}$$

Attachment:
mugeYL1.png

Each angle of ABCDEF is 120 degree.

O is the center of triangle ACE. We have $$\widehat{AOE} =\widehat{COE} = \widehat{AOC} = 120^o$$

We could easily have $$\Delta AFE = \Delta EDC = \Delta CBA = \Delta AOC = \Delta COE = \Delta EOA$$
Hence $$S_{ AFE} = S_{ EDC} = S_{ CBA} = S_{AOC} = S_{COE} = S_{EOA}$$

OD cuts EC at M. Triangle OEC is an equilateral triangle. Hence $$S_{OCD}=\frac{1}{2} \times a \times \frac{a\sqrt{3}}{2}=\frac{a^2\sqrt{3}}{4}$$

Hence $$S_{OEDC}=2S_{OCD}=2 \times \frac{a^2\sqrt{3}}{4} = \frac{a^2\sqrt{3}}{2}$$
So $$S_{OEC}=\frac{1}{2} S_{OEDC} =\frac{1}{2} \times \frac{a^2\sqrt{3}}{2} = \frac{a^2\sqrt{3}}{4}$$

$$S_{AEDC}=4S_{OEC}=4 \times \frac{a^2\sqrt{3}}{4}=a^2\sqrt{3}$$

May I suggest another approach (probably not precise as yours, but it also worked in this case):
The area of a regular hexagon is (3sqrt{3}a^2)/2.
We see that there are 6 equal triangles (AOE=AFE=EOC=EDC...) and that 4 of them are part of ACDE. Therefore I suggest we have to multiply the area of the hexagon by 4/6 or 2/3: ((3sqrt{3}a^2)/2)*2/3=sqrt{3}a^2
Intern
Joined: 08 May 2011
Posts: 21
Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

01 Jun 2017, 14:44
niteshwaghray wrote:
Find the area of AEDC, if ABCDEF is a regular hexagon with each side being equal to “a” units.

A. $$\frac{√3a^2}{4}$$
B. $$\frac{3√3a^2}{4}$$
C. $$√3a^2$$
D. $$\frac{5√3a^2}{4}$$
E. $$\frac{7√3a^2}{4}$$

I used sample numbers to solve:

1) Split up the hexagon into 6 equilateral triangles (something you should know for the exam)

2) Each side has length "a" so I replaced "a" with an easy number "2"

3) Find the area of one of the equilateral triangles with side "2" (a formula you should know) which ends up giving an area of $$\sqrt{3}$$

4) Realize that the AEDC contains exactly 4 equilateral triangles each with area $$\sqrt{3}$$ .. There's a few ways to realize how many equilateral triangles there are... but i think it's safe to assume that the GMAT wouldn't give you a weird shape to find the area

5) Answer = 4 * $$\sqrt{3}$$
Intern
Joined: 13 May 2017
Posts: 3
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

01 Jun 2017, 16:02
Hello
Could you tell me how you figured out that there were 4 equilateral triangles in AEDC? thanks
Intern
Joined: 08 May 2011
Posts: 21
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

02 Jun 2017, 09:24
Hello
Could you tell me how you figured out that there were 4 equilateral triangles in AEDC? thanks

See the attached picture.
Attachments

Untitled.jpg [ 64.4 KiB | Viewed 5877 times ]

Manager
Joined: 23 May 2017
Posts: 240
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

02 Jun 2017, 11:21
Attachment:

FullSizeRender (9).jpg [ 51.25 KiB | Viewed 5864 times ]

Used some trigonometric functions such as

Area of a triangle can be written as = 1/2 side1 * side 2 * angle containing side 1 * side 2
_________________

If you like the post, please award me Kudos!! It motivates me

Manager
Joined: 12 Feb 2017
Posts: 70
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

10 Nov 2017, 05:11
If you are aware of trigonometric concepts, you can solve this sum within a minute.

Area of a triangle = 1/2 * product of two sides * Sin(angle between them)
Attachments

abc.jpg [ 2.01 MiB | Viewed 5088 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 9894
Re: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b  [#permalink]

### Show Tags

11 Feb 2019, 22:10
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: Find the area of AEDC, if ABCDEF is a regular hexagon with each side b   [#permalink] 11 Feb 2019, 22:10
Display posts from previous: Sort by