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What is the area of the quadrilateral ABCD?

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

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New post 03 Dec 2018, 02:36
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (02:08) correct 24% (02:21) wrong based on 63 sessions

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

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New post 03 Dec 2018, 02:50
2
extend the point D till (11,1) call it as X.
And Extend B till (11,7) call it as Y.
Now we have a rectangle of area 10*6 = 60.
Now area of the triangle XDC = 1/2*6*4 = 12.
Now area of the triangle YBC = 1/2*10*2 = 10.
Now area of quadrilateral = 60-12-10 = 38.

D is the answer.

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

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New post 03 Dec 2018, 03:20
Bunuel wrote:
Image
What is the area of the quadrilateral ABCD?

A. 19
B. 31
C. 32
D. 38
E. 76

Attachment:
figure 8.jpg


I solved using approximation.

its a trapezoid
two lengths of bases are 4 & sqrt104 ~10
and height 6

so area : 0.5*6*(4+10)
~42 closest option is D IMO 38...
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Re: What is the area of the quadrilateral ABCD?  [#permalink]

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New post 05 Dec 2018, 08:54
Archit3110 wrote:
Bunuel wrote:
Image
What is the area of the quadrilateral ABCD?

A. 19
B. 31
C. 32
D. 38
E. 76

Attachment:
figure 8.jpg


I solved using approximation.

its a trapezoid
two lengths of bases are 4 & sqrt104 ~10
and height 6

so area : 0.5*6*(4+10)
~42 closest option is D IMO 38...


Could you please elaborate your solution?
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Re: What is the area of the quadrilateral ABCD?  [#permalink]

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New post 05 Dec 2018, 08:56
ParthSanghavi wrote:
Archit3110 wrote:
Bunuel wrote:
Image
What is the area of the quadrilateral ABCD?

A. 19
B. 31
C. 32
D. 38
E. 76

Attachment:
figure 8.jpg


I solved using approximation.

its a trapezoid
two lengths of bases are 4 & sqrt104 ~10
and height 6

so area : 0.5*6*(4+10)
~42 closest option is D IMO 38...


Could you please elaborate your solution?


use distance formula to find the sides of bases & height .. you would get the values
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Re: What is the area of the quadrilateral ABCD?  [#permalink]

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New post 31 Mar 2020, 06:09
Bunuel wrote:
Image
What is the area of the quadrilateral ABCD?

A. 19
B. 31
C. 32
D. 38
E. 76

Attachment:
figure 8.jpg


Area of ABD = 1/2 * 6 * 4 = 12
Area of BCD = 26; Using discriminant method

Area of ABCD = 12 + 26 = 38

IMO D
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Re: What is the area of the quadrilateral ABCD?   [#permalink] 31 Mar 2020, 06:09
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