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What is the area of triangle EBC?

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

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New post 17 Sep 2010, 03:26
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28% (01:41) correct 72% (01:52) wrong based on 137 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.

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

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New post 17 Sep 2010, 03:35
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rafi wrote:
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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.

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

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New post 27 Jul 2016, 20:07
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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

(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
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Re: What is the area of triangle EBC?  [#permalink]

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New post 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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New post 14 Apr 2018, 21:05
Hi guys
a very nice question and I wonder if this is applicable for all the trapezium?
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Re: What is the area of triangle EBC?  [#permalink]

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New post 14 Apr 2018, 21:38
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Rishi91 wrote:
Hi guys
a very nice question and I wonder if this is applicable for all the trapezium?


Rishi91
Yes,this is applicable to all the trapezium.

Actually Trapezium is one of subset of cases, where below theorem is applicable.
Triangles on the same base (or equal bases) and between the same parallels are equal in area
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Re: What is the area of triangle EBC?  [#permalink]

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New post 14 Apr 2018, 22:12
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Hi

This is a classic example of an easy question , but I took around 1 minute to answer it. :(
I realized that this question depends on a simple concept which can b overlooked sometimes making us to fall in trap or to take longer time than required.

I am thinking to start making notes for key concept, and keep it handy so that the chances of trap or longer time to attempt would be minimize. :angel:

Here is the Key Concept.
In any Trapezium, the area of opposite triangles formed by intersection of diagonals and non parallel side are equal.
but the other 2 triangles with parallel sides are NOT equal, they would be equal in case of Parallelogram.

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

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New post 16 Apr 2018, 09:57
gmatbusters Thanks man, learned something after long.
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Re: What is the area of triangle EBC?  [#permalink]

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New post 05 Jul 2019, 12:47
Areas of triangle ADC and BDC are equal, as the triangles are on the same base and between the same parallels.

(1) The area of ΔAED is 16 and ΔDEC is common to both ΔADC and ΔBDC, therefore area of Δ EBC = 16. sufficient.

(2) The area of ΔDEC is 12, it only gives information regarding ΔDEC and no information about ΔEBC. Insufficient.

A is correct.
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Re: What is the area of triangle EBC?   [#permalink] 05 Jul 2019, 12:47
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