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# What is the area of triangle EBC?

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Manager
Joined: 04 Jun 2010
Posts: 109
Concentration: General Management, Technology
Schools: Chicago (Booth) - Class of 2013
GMAT 1: 670 Q47 V35
GMAT 2: 730 Q49 V41
What is the area of triangle EBC? [#permalink]

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17 Sep 2010, 03:26
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95% (hard)

Question Stats:

34% (00:43) correct 66% (01:16) wrong based on 160 sessions

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What is the area of triangle EBC?

(1) The area of ΔAED is 16.

(2) The area of ΔDEC is 12.

[Reveal] Spoiler:
Attachment:

T88956.png [ 5.78 KiB | Viewed 4075 times ]
[Reveal] Spoiler: OA

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Re: What is the area of triangle EBC? [#permalink]

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17 Sep 2010, 03:35
3
KUDOS
rafi wrote:

What is the area of triangle EBC?

(1) The area of ΔAED is 16.

(2) The area of ΔDEC is 12.

How do you solve this question?

Note that area of ADC and BDC is the same (common base and and since AB is parallel to CD, same perpendicular distance to base CD from A and B)

Area(BEC) = Area(BDC) - Area(EDC)
Area(AED) = Area(ADC) - Area(EDC)
=> Area(BEC)=Area(AED)

(1) --> Clearly sufficient
(2) --> Not sufficient, there is no relationship between Area(EDC) and Area(BEC) directly, without any extra knowledge
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Manager
Joined: 07 Jul 2016
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What is the area of triangle EBC? [#permalink]

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27 Jul 2016, 20:07
Since it took me a long time to understand the above reply (kudos given), my clarification:

$$\text{Area of a Triangle}: \frac{1}{2} \times \text{base} \times \text{height}$$
$$ADC$$ and $$BDC$$ share a base ($$DC$$).
$$ADC$$ and $$BDC$$ have the same height as we can determine $$AD$$ and $$BC$$ are parallel (due to the two right angles).

Therefore areas of $$ADC$$ and $$BDC$$ are equal.

(1) The area of ΔAED is 16.

The area of ADC = BDC (given above).
Using visual area subtraction
AED = ADC - DEC
BEC = BDC - DEC

Therefore the area of AED = BEC.

Sufficient

(2) The area of ΔDEC is 12.

This information cannot be used to obtain anything more as we cannot determine side lengths or angles from the information.

Insufficient

[Reveal] Spoiler:
(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

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Manager
Joined: 21 Jun 2016
Posts: 96
Location: India
Re: What is the area of triangle EBC? [#permalink]

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28 Jul 2016, 03:48
Very good question. This forum is superb.
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Re: What is the area of triangle EBC? [#permalink]

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26 Sep 2017, 20:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the area of triangle EBC?   [#permalink] 26 Sep 2017, 20:41
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# What is the area of triangle EBC?

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