Last visit was: 12 Jul 2024, 21:02 It is currently 12 Jul 2024, 21:02
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In the figure above, lines L and P are parallel. The segment AD is the

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640203 [8]
Given Kudos: 84576
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3649 [6]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Intern
Joined: 16 Dec 2013
Posts: 25
Own Kudos [?]: 15 [5]
Given Kudos: 41
Location: United States
GPA: 3.7
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640203 [3]
Given Kudos: 84576
Re: In the figure above, lines L and P are parallel. The segment AD is the [#permalink]
2
Kudos
1
Bookmarks
Bunuel wrote:

In the figure above, lines L and P are parallel. The segment AD is the same length as the segment DC; AD is parallel to BC. If the length of AD is equal to 4, and angle ADC is equal to 60º, what is the area of ABCD?

A. 4√2
B. 4√3
C. 8√2
D. 8√3
E. 16√2

Kudos for a correct solution.

Attachment:
parallel.gif

800score Official Solution:

AB is parallel to DC and AD is parallel to BC, so ABCD is parallelogram. We know how to find the area of a parallelogram we multiply the height of parallelogram by its base length.

We are told that the angle ADC is a 60º angle. If we draw an altitude from A straight down and perpendicular to line P, the length of that altitude will be equal to the height of the parallelogram. Moreover, it forms a 60-30-90 triangle, so we can easily find its length. Since the hypotenuse of that triangle is equal to 4, the second longest side must be equal to 2√3 (since the proportions for the triangle run x, x√3, and 2x).

To find the area of a parallelogram , multiply the height of the parallelogram by its base length: 4 × 2√3 = 8√3, or answer choice (D).
Non-Human User
Joined: 09 Sep 2013
Posts: 33955
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: In the figure above, lines L and P are parallel. The segment AD is the [#permalink]
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 the figure above, lines L and P are parallel. The segment AD is the [#permalink]
Moderator:
Math Expert
94302 posts