GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 03:28

### 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

# Triangle BDC is an equilateral triangle and triangle ABC is a right tr

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60647
Triangle BDC is an equilateral triangle and triangle ABC is a right tr  [#permalink]

### Show Tags

05 Sep 2018, 00:06
1
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:25) correct 31% (02:37) wrong based on 86 sessions

### HideShow timer Statistics

Triangle BDC is an equilateral triangle and triangle ABC is a right triangle. If line segment DC is 6 units in length, what is the area of the shaded region?

A. 9

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

C. 18

D. $$18\sqrt{2}$$

E. $$18\sqrt{3}$$

Attachment:

image023.jpg [ 2.71 KiB | Viewed 1336 times ]

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 980
WE: Supply Chain Management (Energy and Utilities)
Triangle BDC is an equilateral triangle and triangle ABC is a right tr  [#permalink]

### Show Tags

05 Sep 2018, 01:17
1
1
Bunuel wrote:

Triangle BDC is an equilateral triangle and triangle ABC is a right triangle. If line segment DC is 6 units in length, what is the area of the shaded region?

A. 9

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

C. 18

D. $$18\sqrt{2}$$

E. $$18\sqrt{3}$$

Attachment:
image023.jpg

Since DBC is an equilateral triangle, so DB=BC=DC=6

So, AC=12. Hence using Pythagorean formula in the right angled triangle ABC, we have $$AB=AC^2-BC^2$$
Or, $$AB=\sqrt{12^2-6^2}=6\sqrt{3}$$
So, area of triangle ABC=$$\frac{1}{2}*6*6\sqrt{3}=18\sqrt{3}$$

Area of equilateral triangle DBC=$$\sqrt{3}/4*6^2$$=$$9\sqrt{3}$$

Area of shaded region=Area of triangle ABC-Area of triangle DBC=$$18\sqrt{3}-9\sqrt{3}=9\sqrt{3}$$

Ans. (B)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4226
Re: Triangle BDC is an equilateral triangle and triangle ABC is a right tr  [#permalink]

### Show Tags

16 Jan 2019, 18:32
Top Contributor
Bunuel wrote:

Triangle BDC is an equilateral triangle and triangle ABC is a right triangle. If line segment DC is 6 units in length, what is the area of the shaded region?

A. 9

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

C. 18

D. $$18\sqrt{2}$$

E. $$18\sqrt{3}$$

Attachment:
image023.jpg

Since ∆BDC is an equilateral triangle, and since ∆ABC is a right triangle, we can add the following to our diagram.

Next, if we add the following perpendicular line . . .

. . . we can add more to our diagram

At this point, we can simplify matters A LOT by recognizing that if we "cut" out the top triangle and rotate it . . .

And keep rotating . . .

. . . it fits nicely here.

At this point, we should see that the shaded area is actually a nifty EQUILATERAL triangle with sides of length 6

Area of an equilateral triangle = (√3)(side²/4)
So, the area of the shaded triangle = (√3)(6²/4)
= (√3)(36/4)
= 9√3

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: Triangle BDC is an equilateral triangle and triangle ABC is a right tr   [#permalink] 16 Jan 2019, 18:32
Display posts from previous: Sort by