It is currently 24 Jun 2017, 22:27

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is

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

### Hide Tags

Senior Manager
Joined: 11 Sep 2005
Posts: 310
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 15:08
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:04) correct 38% (01:18) wrong based on 306 sessions

### HideShow timer Statistics

Attachment:
File comment: PS-SET22 Q8 PARALLELOGRAM

PS-SET22 Q8.GIF [ 2.06 KiB | Viewed 12035 times ]
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3
[Reveal] Spoiler: OA
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 15:24
singh_amit19 wrote:
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3

Ok if you look at the first triangle. the one with one side =4..we know its a 30-60-90 triangle

so based on that we know that side opposite 30 is (sqrt(3)*x)

we know x=2 so we know that the height is sqrt(3)*2

we know the base is 6, height is sqrt(3)2 area= base*height

12sqrt(3)
Director
Joined: 11 Jun 2007
Posts: 914
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 15:30
1
This post was
BOOKMARKED
fresinha12 wrote:
singh_amit19 wrote:
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3

Ok if you look at the first triangle. the one with one side =4..we know its a 30-60-90 triangle

so based on that we know that side opposite 30 is (sqrt(3)*x)

we know x=2 so we know that the height is sqrt(3)*2

we know the base is 6, height is sqrt(3)2 area= base*height

12sqrt(3)

30:60:90
x: √3: 2x
2: 2√3: 4<-given to us

i get 2√3 for part of my base. the height i got was 2

height * base = 2*6 = 12
even when i did it the long way of adding the two triangles with the quad in the middle i was able to deduce the answer to 12

Last edited by beckee529 on 09 Oct 2007, 21:05, edited 1 time in total.
Director
Joined: 08 Jun 2007
Posts: 573
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 20:55
singh_amit19 wrote:
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3

B .
easy if you know some formulas of triginometry

sin(30) = 1/2 = height/hypetenuse(4) => height = 2
area = base * height = 2*6=12
Director
Joined: 11 Jun 2007
Posts: 914
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 21:07
ashkrs wrote:
singh_amit19 wrote:
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3

B .
easy if you know some formulas of triginometry

sin(30) = 1/2 = height/hypetenuse(4) => height = 2
area = base * height = 2*6=12

nice one! hhahaah.. dont remember much about this.. took trig well over 10 years ago freshmen year of HS
Director
Joined: 12 Jun 2006
Posts: 532
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 21:39
I get E.

triangle is 30:60:90 ==> x:x(sqrt)3:2x ==> 2:2(sqrt)3:4

area(triangle)=2(sqrt)3*2/2 = 2(sqrt)3

6 [parallelogram base] - 2(sqrt)3 [triangle base] = 4(sqrt)3 [trapezoid base]

area(trapezoid)=6+4(sqrt)3*2/2 = 10(sqrt)3

10(sqrt)3 + 2(sqrt)3 = 12(sqrt)3
Director
Joined: 11 Jun 2007
Posts: 914
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 21:49
this is how i got 12 by finding the 3 subparts (by drawing two lines to create two triangles and quadrilateral):

30:60:90
x: √3: 2x
2: 2√3: 4

h = 2,
base of triangle => b = 2√3,
base of quad => B = 6 - 2√3

area of two triangles = 2 * 1/2 b*h
= 2 [ 1/2 * 2 * 2√3 ] = 4√3

area of middle part (quad) = B * h
(6 - 2√3) * 2 = 12 - 4√3

adding the two together:
4√3 + 12 - 4√3 = 12 B
Director
Joined: 12 Jun 2006
Posts: 532
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 22:09
Quote:
area of middle part (quad) = B * h
(6 - 2√3) * 2 = 12 - 4√3

aren't we solving what's inside the parentheses first?
6 - 2√3 = 4√3
4√3 * 2 = 8√3
should we be using the distributive property here?
Director
Joined: 11 Jun 2007
Posts: 914
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 22:21
ggarr wrote:
Quote:
area of middle part (quad) = B * h
(6 - 2√3) * 2 = 12 - 4√3

aren't we solving what's inside the parentheses first?
6 - 2√3 = 4√3
4√3 * 2 = 8√3
should we be using the distributive property here?

6 - 2√3 does not = to 4√3!!
6√3 - 2√3 = 4√3
use a calculator and you will see the difference
and i did use distributive property
(6 - 2√3) * 2 =
6*2 - 2√3*2 =
12 - 4√3
Director
Joined: 09 Aug 2006
Posts: 755
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

09 Oct 2007, 23:42
singh_amit19 wrote:
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8√3
E. 12√3

B.

The right triangle w/ hypotenuese PQ is a 30, 60, 90 triangle with sides a, sqrt 2a and 2a.

Side 2a corresponds to 4.
2a = 4
a = 2

a is the shortest side, therefore facing the smallest angle which is P. Therefore 2 is the height.

ar = b*h = 12
Manager
Joined: 25 Jul 2010
Posts: 140
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

11 Sep 2010, 14:27
beckee529 wrote:
this is how i got 12 by finding the 3 subparts (by drawing two lines to create two triangles and quadrilateral):

30:60:90
x: √3: 2x
2: 2√3: 4

Is it mandatory to mug up this rule regarding 30:60:90 triangle?
No other ways of solving this problem? Isn't it correct that opposite sides of angles 30 and 60 are in ratio 1:2?

Any help is appreciated.
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

11 Sep 2010, 14:49
4
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Orange08 wrote:
beckee529 wrote:
this is how i got 12 by finding the 3 subparts (by drawing two lines to create two triangles and quadrilateral):

30:60:90
x: √3: 2x
2: 2√3: 4

Is it mandatory to mug up this rule regarding 30:60:90 triangle?
No other ways of solving this problem? Isn't it correct that opposite sides of angles 30 and 60 are in ratio 1:2?

Any help is appreciated.

• A right triangle where the angles are 30°, 60°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio $$1 : \sqrt{3}: 2$$.
Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

BACK TO THE ORIGINAL QUESTION:

Now, as hypotenuse PQ (the largest side) equals to 4 then the side opposite 30 degrees (smallest side, which is also the height of the parallelogram) equals to 4/2=2. Thus area of parallelogram is height*base=2*6=12.

Answer: B.

For more on this issues check Triangles chapter of Math Book (link in my signature).

Hope it helps.
_________________
Manager
Joined: 25 Jul 2010
Posts: 140
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

11 Sep 2010, 14:55
Sounds assuring. Thanks a lot Bunuel.
Senior Manager
Joined: 20 Jul 2010
Posts: 263
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

11 Sep 2010, 15:23
Thanks Bunuel for the triangle. I was deciding on what is sin 30 to get height. I was confused in 1/2 and sqrt(3)/2
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

11 Sep 2010, 22:32
saxenashobhit wrote:
Thanks Bunuel for the triangle. I was deciding on what is sin 30 to get height. I was confused in 1/2 and sqrt(3)/2

Trigonometry is not tested on GMAT, so any GMAT geometry question can be solved without it.

Anyway: The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Sin (30 degrees)= cos (60 degrees) = 1/2 --> in out case: sin(30 degrees)=height/PQ=height/4=1/2 --> height=2.
_________________
Manager
Joined: 20 Apr 2010
Posts: 210
Schools: ISB, HEC, Said
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

13 Sep 2010, 06:33
Bunuel

Are we supposed to remeber the corelations for the standard triangles
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

13 Sep 2010, 08:33
prashantbacchewar wrote:
Bunuel

Are we supposed to remeber the corelations for the standard triangles

Yes, I think it's good to know below 2 cases:

• A right triangle where the angles are 30°, 60°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio $$1 : \sqrt{3}: 2$$.
Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

• A right triangle where the angles are 45°, 45°, and 90°.

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should also commit to memory is: The sides are always in the ratio $$1 : 1 : \sqrt{2}$$. With the $$\sqrt{2}$$ being the hypotenuse (longest side). This can be derived from Pythagoras' Theorem. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles.
• Area of a 45-45-90 triangle. As you see from the figure above, two 45-45-90 triangles together make a square, so the area of one of them is half the area of the square. As a formula $$A=\frac{S^2}{2}$$. Where S is the length of either short side.

For more on this issues check Triangles chapter of Math Book (link in my signature).

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15960
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

19 Nov 2014, 02:18
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15960
Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]

### Show Tags

21 Apr 2016, 22:56
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: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is   [#permalink] 21 Apr 2016, 22:56
Similar topics Replies Last post
Similar
Topics:
5 PQRS is a parallelogram and ST = TR. What is the ratio of the area of 3 16 May 2016, 13:15
52 The parallelogram shown has four sides of equal length. What is the 14 30 May 2017, 22:44
13 The ratio (p + q):(r + p):(q + r) = 3:4:10. (p + q + r) = 34. What is 7 12 Mar 2017, 10:15
46 In triangle PQR, the angle Q = 9, PQ = 6 cm, QR = 8 cm. X is 18 07 May 2017, 14:32
13 In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which 13 13 Feb 2016, 02:40
Display posts from previous: Sort by

# In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is

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

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.