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# What is the area of quadrilateral ABCD?

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Math Expert
Joined: 02 Sep 2009
Posts: 56307

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18 Sep 2018, 22:10
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Difficulty:

65% (hard)

Question Stats:

48% (01:21) correct 52% (01:23) wrong based on 26 sessions

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What is the area of quadrilateral ABCD?

(1) l^2 + 2lw + w^2 = 16
(2) l^2 – 2lw + w^2 = 4

Attachment:

image004.jpg [ 1.59 KiB | Viewed 360 times ]

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18 Sep 2018, 22:47
Bunuel wrote:

What is the area of quadrilateral ABCD?

(1) l^2 + 2lw + w^2 = 16
(2) l^2 – 2lw + w^2 = 4

Attachment:
image004.jpg

Notice that the type of quadrilateral is not mentioned explicitly or implicitly neither in the question stem nor in the statements.

Also, notations l and w are provided for two sides only . Measure of other 2 sides of the quadrilateral may be any value.
Hence , combined also we don't have any additional info on measurement of angle if any other property of the quadrilateral ,which would ensure unique measure of area of the quadrilateral.

Therefore, insufficient.

Ans (E)

P.S. As per official guide, figures confirm to the information given in the question.
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19 Sep 2018, 03:32
Given:
• AD = l and DC = w

To find:
• The area of the quadrilateral, ABCD

Analysing Statement 1
“$$l^2 + 2lw + w^2 = 16$$”

• Implies, l + w = 4

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, Statement 1 is NOT sufficient to arrive at a unique answer

Analysing Statement 2
“$$l^2 - 2lw + w^2 = 4$$”

• Implies, l – w = 2

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, Statement 2 is NOT sufficient to arrive at a unique answer

Combining Both Statements
• From Statement 1, we know, l + w = 4
• From Statement 2, we know, l - w = 2
• Solving the above equations, we get, l = 3 and w = 1

However, we cannot infer anything about the other two sides of the quadrilateral.

So, we cannot find the area of ABCD

Therefore, both statements TOGETHER are NOT sufficient to arrive at a unique answer

Hence, the correct answer is option E.

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Re: What is the area of quadrilateral ABCD?   [#permalink] 19 Sep 2018, 03:32
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