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
Question Stats:
62% (02:04) correct
38% (01:18) wrong based on 306 sessions
HideShow timer Statistics
Attachment: File comment: PSSET22 Q8 PARALLELOGRAM
PSSET22 Q8.GIF [ 2.06 KiB  Viewed 12032 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
Official Answer and Stats are available only to registered users. Register/ Login.



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 306090 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 306090 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)*2we 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: 39626

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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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: 39626

Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is [#permalink]
Show Tags
11 Sep 2010, 22:32



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: 39626

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 454590 triangle. As you see from the figure above, two 454590 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is
[#permalink]
21 Apr 2016, 22:56








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


5


PQRS is a parallelogram and ST = TR. What is the ratio of the area of

Bunuel 
3 
16 May 2016, 13:15 

52


The parallelogram shown has four sides of equal length. What is the

Bunuel 
14 
30 May 2017, 22:44 

13


The ratio (p + q):(r + p):(q + r) = 3:4:10. (p + q + r) = 34. What is

desaichinmay22 
7 
12 Mar 2017, 10:15 

46


In triangle PQR, the angle Q = 9, PQ = 6 cm, QR = 8 cm. X is

Qoofi 
18 
07 May 2017, 14:32 

13


In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5. Which

hrish88 
13 
13 Feb 2016, 02:40 



