It is currently 18 Mar 2019, 15:26

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

What is the area of the quadrilateral shown above?

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5811
Followers: 93

Kudos [?]: 1138 [0], given: 5418

What is the area of the quadrilateral shown above? [#permalink]  07 Jun 2017, 01:52
Expert's post
00:00

Question Stats:

86% (01:03) correct 13% (01:34) wrong based on 36 sessions

Attachment:

#GREpracticequestion What is the area of the quadrilateral shown above .jpg [ 6.78 KiB | Viewed 891 times ]

What is the area of the quadrilateral shown above?

A) $$2 \sqrt{3}$$

B) $$3 \sqrt{3}$$

C) $$6$$

D) $$6 \sqrt{3}$$

E) $$8$$
[Reveal] Spoiler: OA

_________________
Intern
Joined: 02 Jan 2018
Posts: 3
Followers: 0

Kudos [?]: 3 [1] , given: 1

Re: What is the area of the quadrilateral shown above? [#permalink]  04 Jan 2018, 21:13
1
KUDOS
Draw a perpendicular forming two right angle triangle, now the figure has two right angle triangle and one rectangle.Both the triangles have same angle so the area will be same.
By using pythagoras theorem find the height of the triangle i.e sqrt(3), now find the area of both the triangle and a rectangle.
sqrt(3)/2+sqrt(3)/2+2*sqrt(3) = 3sqrt(3)
Intern
Joined: 21 Dec 2017
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 1

Re: What is the area of the quadrilateral shown above? [#permalink]  11 Jan 2018, 00:51
1
KUDOS
Consider three equilateral triangles within quadrilateral,each with side measuring 2.Now Area for Equilateral triangle is (sqrt(3)/4)*(side)^2 and multiply it by 3 to get area for three equilateral triangle i.e whole quadrilateral.
Manager
Joined: 02 Jan 2018
Posts: 66
Followers: 0

Kudos [?]: 30 [0], given: 0

Re: What is the area of the quadrilateral shown above? [#permalink]  23 Jan 2018, 10:45
Moderator
Joined: 18 Apr 2015
Posts: 5811
Followers: 93

Kudos [?]: 1138 [0], given: 5418

Re: What is the area of the quadrilateral shown above? [#permalink]  23 Jan 2018, 15:28
Expert's post
Added the OA. It is B.

Regards
_________________
Director
Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 21 [0], given: 1

Re: What is the area of the quadrilateral shown above? [#permalink]  20 Jan 2019, 16:27
mayurwaghela wrote:
By using pythagoras theorem find the height of the triangle i.e sqrt(3),

How?
Director
Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 21 [0], given: 1

Re: What is the area of the quadrilateral shown above? [#permalink]  20 Jan 2019, 16:30
Can we think it as a trapezium?
Intern
Joined: 02 Jan 2019
Posts: 13
Followers: 0

Kudos [?]: 2 [0], given: 9

Re: What is the area of the quadrilateral shown above? [#permalink]  23 Jan 2019, 07:43
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.
Re: What is the area of the quadrilateral shown above?   [#permalink] 23 Jan 2019, 07:43
Display posts from previous: Sort by