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# In the figure above, if the perimeter of quadrilateral ABCD is 24, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 43785
In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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04 Oct 2017, 10:13
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In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

[Reveal] Spoiler:
Attachment:

2017-10-04_1123_002.png [ 8.04 KiB | Viewed 1223 times ]
[Reveal] Spoiler: OA

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Joined: 25 Feb 2013
Posts: 919
Location: India
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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04 Oct 2017, 10:29
1
KUDOS
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-04_1123_002.png

As $$BC || AD$$, angle $$BCE=CED=x°$$. Hence triangle $$ECD$$ is isosceles with $$CE=CD=5$$

Given perimeter of $$ABCD=24$$, so $$AD=24-(3+6+5)=10$$

$$ED=AD-AE=10-2=8$$

Height of triangle $$ECD = AB = 3$$ and Base $$ED=8$$

So area $$= \frac{1}{2}*3*8=12$$

Option A
Senior Manager
Joined: 24 Apr 2016
Posts: 333
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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04 Oct 2017, 10:39
1
KUDOS
As BC is parallel to AD, Angle BCE = Angle CED = X

Since Angles BCE & CED are equal, Triangle ECD is isosceles, therefore CD = EC = 5

Perimeter of ABCD = AB + BC + CD + AE + ED = 3 + 6 + 5 + 2 + ED = 24 ==> ED = 8

Height of Triangle ECD is 3

Area of Triangle ECD = $$\frac{1}{2}$$ * 8 * 3 = 12

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Intern
Joined: 01 May 2017
Posts: 4
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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03 Nov 2017, 10:58
Bunuel can you explain how 24?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 919
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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03 Nov 2017, 18:41
bara25 wrote:
Bunuel can you explain how 24?

Hi Bunuel

I agree with bara25. Kindly provide the OA or can you highlight the errors in my approach. IMO answer should be 12
Intern
Joined: 29 May 2012
Posts: 39
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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03 Nov 2017, 19:28
I can't work out 24 either. My answer is A like many of you. Awaiting for the OA.
Math Expert
Joined: 02 Aug 2009
Posts: 5647
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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03 Nov 2017, 19:42
1
KUDOS
Expert's post
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-04_1123_002.png

hi Bunuel
there seems to be some typo..
Either the answer is for AREA of trapezium ABCD.. then it is 24
or typo in OA, as ans should be 12
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Math Expert
Joined: 02 Sep 2009
Posts: 43785
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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03 Nov 2017, 22:35
chetan2u wrote:
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

[Reveal] Spoiler:
Attachment:
2017-10-04_1123_002.png

hi Bunuel
there seems to be some typo..
Either the answer is for AREA of trapezium ABCD.. then it is 24
or typo in OA, as ans should be 12

The OA is A. Edited. Sorry for that.
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Posts: 121
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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04 Nov 2017, 07:45
darn it:)) I killed myself yesterday, solved for A in 1 min, the OA was 24, and spent like 1h trying to figure out how the hell on earth that can be 24 ) solved like in 3 different way, 12 again
Intern
Joined: 08 Aug 2017
Posts: 24
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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17 Nov 2017, 02:36
Question needs more information because given information doesn't means neither that AD II BC nor AB is perpendicular to AD.
Provided information is not sufficient to reach at answer.
Math Expert
Joined: 02 Aug 2009
Posts: 5647
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha [#permalink]

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17 Nov 2017, 03:31
gvij2017 wrote:
Question needs more information because given information doesn't means neither that AD II BC nor AB is perpendicular to AD.
Provided information is not sufficient to reach at answer.

Hi..
It is clearly given that AB is perpendicular to AD by showing sign of L at the angle. A squarish box at the angle tells us that angle is 90..
Also if two sides on the base are 90°, the two sides will be perpendicular since both are at same angle.

Seems you are misunderstanding something
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha   [#permalink] 17 Nov 2017, 03:31
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# In the figure above, if the perimeter of quadrilateral ABCD is 24, wha

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