In parallelogram PQRS shown, if PQ=4 and QR=6...

Expert replies

swerve: Legendary Member; Posts: 2548; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Jan 07, 2018 6:30 am

https://postimg.cc/image/846wtwfxh/ (zoom here)

In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8âˆš3
E. 12âˆš3

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it of the following way but I'm not sure,

I know that the area of a parallelogram is,
$$A_p=b\cdot h$$
Then, I can determine h of,
$$\sin\ 30\ =\frac{h}{4}$$
Finally, QR will be equal to PS and with that I can determine the area, right?

I need your help. Thanks.

Like this post

Source: Beat The GMAT — Problem Solving | Sun Jan 07, 2018 6:30 am

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sun Jan 07, 2018 3:34 pm

You never need trigonometry to solve GMAT problems!

You're right: the area of a parallelogram = b*h.

The base is easy: QR and PS are both bases, equal to 6.

The height will be the perpendicular line from point Q to the base PS. Since we're given that angle QPS = 30*, we know that we have a 30 : 60 : 90 right triangle. Remember that in a 30 : 60 : 90 triangle, the ratio of the side lengths is x : x(sqrt{3}) : 2x

If the hypotenuse PQ = 4, that represents our 2x side. The side across from the 30* angle is the x side, so the height = 2.

b*h = 6*2 = 12

The answer is B.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Aug 12, 2019 10:44 am

swerve wrote:

https://postimg.cc/image/846wtwfxh/ (zoom here)

In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?

A. 8
B. 12
C. 24
D. 8âˆš3
E. 12âˆš3

Let T be the intersection of the height of the parallelogram and its base. We see that triangle PQT is a 30-60-90 right triangle. Since the height of the triangle (or the parallelogram), QT, is opposite the 30-degree angle, it's half the hypotenuse of the triangle, PQ. So QT = Â½(PT) = Â½(4) = 2.

Since the area of a parallelogram is the product of its height and its base, the area of parallelogram PQRS is 2 x 6 = 12.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review