Last visit was: 05 Nov 2024, 06:01 It is currently 05 Nov 2024, 06:01

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29891
Own Kudos [?]: 36119 [1]
Given Kudos: 25919
Send PM
avatar
Intern
Intern
Joined: 02 Jan 2018
Posts: 3
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 21 Dec 2017
Posts: 1
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
avatar
Manager
Manager
Joined: 02 Jan 2018
Posts: 66
Own Kudos [?]: 39 [0]
Given Kudos: 0
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
Answer for this please. I am getting 3\sqrt{3} as my answer.
Verbal Expert
Joined: 18 Apr 2015
Posts: 29891
Own Kudos [?]: 36119 [0]
Given Kudos: 25919
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
Expert Reply
Added the OA. It is B.

Regards
avatar
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 133 [0]
Given Kudos: 0
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
mayurwaghela wrote:
By using pythagoras theorem find the height of the triangle i.e sqrt(3),

How?
avatar
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 133 [0]
Given Kudos: 0
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
Can we think it as a trapezium?
avatar
Intern
Intern
Joined: 02 Jan 2019
Posts: 14
Own Kudos [?]: 21 [0]
Given Kudos: 0
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
2
Yes it can be considered as a trapezoid, since the two angles alpha are the same and are connected to the longer of the two bases.

Area: 0.5(Base 1 + Base 2) * height.

How do we get the height? The shorter base (length 2) must have its center where the longer base has its center due to the fact that both angles are equal. Thus, we derive that the longer base just extends the shorter base by (4-2 = 2). Split equally on each side, we can see the longer base composition of lengths 1 + 2 + 1.

If we look at the left part of the figure we have the upward sloping line with length 2. If we let fall a perpendicular from the connection of the upward sloping line and its vertex with the shorter base, we arrive exactly at the first part of the 1 + 2 + 1 composition of the longer base.

Thus we have a created triangle with a base 1 and hypotenuse 2. Since we also know that it has a 90-degree angle, we can deduct it must be a 30 - 60 - 90 triangle. (Remainder: Side lengths of a 30 - 60 - 90 triangle are 1:2:sqrt(3). Thus the height of the triangle is sqrt(3) which equals the height of the trapezoid.

Plug in the formula.

Area : 1/2*6* √3 = 3√3
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: What is the area of the quadrilateral shown above? [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: What is the area of the quadrilateral shown above? [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne