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What is the area of quadrilateral ABCD?

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What is the area of quadrilateral ABCD?  [#permalink]

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New post 04 Feb 2019, 03:43
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A
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C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:50) correct 30% (01:30) wrong based on 23 sessions

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What is the area of quadrilateral ABCD?

A. 38
B. 40
C. 42
D. 44
E. 45


Attachment:
#GREpracticequerstion What is the area of quadrilateral ABC.jpg
#GREpracticequerstion What is the area of quadrilateral ABC.jpg [ 20.15 KiB | Viewed 385 times ]

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What is the area of quadrilateral ABCD?  [#permalink]

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New post Updated on: 04 Feb 2019, 04:34
Bunuel wrote:
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What is the area of quadrilateral ABCD?

A. 38
B. 40
C. 42
D. 44
E. 45


Extend the line c down to x axis and let point D meet the perpedicular of pt C at E
Triangle DCE x=6 & y = 4
rectangle = AFCE ; length = 10 & width = 4
triangle BFC= height = 10 and base = 2

0.5*2*10 +10*4- 0.5*6*4= 38
IMO A
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Originally posted by Archit3110 on 04 Feb 2019, 03:48.
Last edited by Archit3110 on 04 Feb 2019, 04:34, edited 1 time in total.
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Re: What is the area of quadrilateral ABCD?  [#permalink]

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New post 04 Feb 2019, 04:21
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Bunuel wrote:
Image
What is the area of quadrilateral ABCD?

A. 38
B. 40
C. 42
D. 44
E. 45


Attachment:
#GREpracticequerstion What is the area of quadrilateral ABC.jpg


Inline is my take, i extended the lines to get a rectangle with length 10 and breadth 6

Total area = 60, now when you extend the lines and make this figure you will get 2 right triangles with dimensions as 4(h),6(b) and 2(h),10(b)

Area = 60 - [1/2 * 4*6 + 1/2 * 2*10]
60 - 22
38

A
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Re: What is the area of quadrilateral ABCD?  [#permalink]

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New post 04 Feb 2019, 04:24
IMO A,

Lets extend the rectangle then the area of rectangle is 60-(1/2*10*2+1/2*6*4)= 38
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Re: What is the area of quadrilateral ABCD?  [#permalink]

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New post 04 Feb 2019, 05:47
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Attachment:
Rectangle.jpg
Rectangle.jpg [ 131.52 KiB | Viewed 228 times ]


Let the given figure be extended to form a rectangle as shown above. Now it is easy to calculate the are of the given figure.

Area of quadrilateral ABCD = Area of rectangle ABEF - Area of triangle BCE - Area of triangle CDF

Area of rectangle ABEF = 10*6 = 60

Area of triangle BCE = \(\frac{1}{2} * 2 * 10\) = 10

Area of triangle CDF = \(\frac{1}{2} * 6 * 4\) = 12

Area of quadrilateral ABCD = 60 - 10 - 12 = 38

OPTION: A
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Re: What is the area of quadrilateral ABCD?  [#permalink]

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New post 04 Feb 2019, 06:38
Bunuel wrote:
Image
What is the area of quadrilateral ABCD?

A. 38
B. 40
C. 42
D. 44
E. 45


Attachment:
#GREpracticequerstion What is the area of quadrilateral ABC.jpg


IMO A.

Draw the line BD, you will get two triangles ABD and BDC.
Area of quadrilateral = A(ABD)+A(BDC)

A(ABD) = 1/2*6*4=12.

By distance formula, BD = \(2\sqrt13\) and CD = \(2\sqrt13\) Therefore, area of BDC = 26.

And A(quadrilateral) = 26+12=38
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Re: What is the area of quadrilateral ABCD?   [#permalink] 04 Feb 2019, 06:38
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