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If ABC is an equilateral triangle and AB||CD, what fraction of the are

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If ABC is an equilateral triangle and AB||CD, what fraction of the are  [#permalink]

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New post 10 Oct 2016, 00:54
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:21) correct 31% (02:36) wrong based on 117 sessions

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If ABC is an equilateral triangle and AB||CD, what fraction of the area of quadrilateral ABDC is shaded?

A. 1/4
B. 1/(2√3)
C. 1/3
D. 1/2
E. 2/3

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Re: If ABC is an equilateral triangle and AB||CD, what fraction of the are  [#permalink]

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New post 10 Oct 2016, 01:35
Height of triangle = Height of quadrilateral ABDC = (sqrt 3/2)x3.
Area of triangle ABC =( sqrt 3/4)x3x3
Area of quadrilateral ABDC = ((3+6)/2)x((sqrt 3/2)x3)

Therefore, ratio of Area of triangle ABC to Area of quadrilateral ABDC = 1/3
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Re: If ABC is an equilateral triangle and AB||CD, what fraction of the are  [#permalink]

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New post 10 Oct 2016, 14:52
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1
Heights of triangle ABC and BCD are equal if we consider AB and CD as their bases.(Since AB || CD)

Let that height be 'h'.

Area of ABC = 0.5*3*h

Area of BCD = 0.5*6*h

Fraction = Area of ABC/(Area of ABC + Area of BCD)

=1.5h/(1.5h+3h) = 1.5h/4.5h = 1/3

C
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Re: If ABC is an equilateral triangle and AB||CD, what fraction of the are  [#permalink]

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New post 08 Feb 2018, 09:34
We actually do not need any calculation here.

We have AB || CD, therefore their perpendicular is equal (draw from either B or C)
base AB = 1/2 base CD => Area of ABC = 1/2 area of BCD

=> The shaded part (ABC) will equal to 1/3 of ABCD (area of ABC + BCD = ABCD)

Answer C
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Re: If ABC is an equilateral triangle and AB||CD, what fraction of the are &nbs [#permalink] 08 Feb 2018, 09:34
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