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655-705 (Hard)|   Geometry|      
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Bunuel
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In the figure above, BC and DE are parallel, and CD and AE are paralle 09 Nov 2017, 23:31
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A
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Difficulty:

65% (hard)

Question Stats:

58% (02:48) correct 42% (03:12) wrong based on 83 sessions

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In the figure above, BC and DE are parallel, and CD and AE are parallel. If AE, AB and CD are 12, 9 and 6 respectively, what is the area of the figure?

(A) 51
(B) 54
(C) 78
(D) 108
(E) cannot be determined


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A
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In the figure above, BC and DE are parallel, and CD and AE are paralle 10 Nov 2017, 00:42
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Following to the reasoning in the attachment, answer should be A.
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In the figure above, BC and DE are parallel, and CD and AE are paralle 10 Nov 2017, 09:33
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As we do not know the slope of BC or DE, the area can not be determined.
Answer is E
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In the figure above, BC and DE are parallel, and CD and AE are paralle 11 Nov 2017, 04:21
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Bunuel

In the figure above, BC and DE are parallel, and CD and AE are parallel. If AE, AB and CD are 12, 9 and 6 respectively, what is the area of the figure?

(A) 51
(B) 54
(C) 78
(D) 108
(E) cannot be determined


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Hi All,

attached my approach. Any quick approach for this question??
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In the figure above, BC and DE are parallel, and CD and AE are paralle 23 Nov 2020, 08:17
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Extend Line BC straight until it interests Line AE. Call this Intersection Point = G

Since we are told CD is Parallel to AE, our created Line segment GE will also be Parallel to CD

We are also told that BC is Parallel to DE. The Extension Line Segment we created of CG will be Parallel to DE

We thus have Divided the Entire Figure into 2 figures:

(1) a Right Triangle BAG

(2) a Parallelogram CGDE

The height of the parallelogram is given by the Straight Line Distance between the 2 Parallel, Opposite Sides CD and GE ———> 4

Rule: Opposite, Parallel Sides are Equal in a parallelogram.

Since we are Given that CD = 6, we know Opposite Side GE = 6. We can use GE as our Base.

Area of Parallelogram GCDE = (Base) * (height) = 6 * 4 = 24


Area of Right Triangle BAG = (1/2) * (AB) * (AG)


Leg AG = (Length of AE 12) - (Length of Parallelogram Side GE 6)

AG = (12) - (6) = 6

AB is Given as = 9

Area of Right Triangle BAG = (1/2) * (6) * (9) = 27


Area of entire figure = 24 + 27 = 51


(A)
51

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In the figure above, BC and DE are parallel, and CD and AE are paralle 24 Nov 2021, 09:16
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