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What is the area of the shaded quadrilateral in the figure above?

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What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 27 Feb 2017, 14:13
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Question Stats:

83% (00:49) correct 17% (01:00) wrong based on 76 sessions

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What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58
[Reveal] Spoiler: OA

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What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 27 Feb 2017, 17:20
Would appreciate other people's feedback on Statement 1, but came about it as follows:

1) X^2 - Y^2 = 40

Even after breaking down into (x+y) * (x-y) = 40, didn't seem to help much. Left it as insufficient.

2) X^2 + Y^2 = 58

Using the pythagorean theorem, broke it down into a^2 + b^2 = c^2. Therefore, c^2 = 58, which is the area of the quadrilateral. Accordingly, B is sufficient.

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Re: What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 28 Feb 2017, 07:54
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Matruco wrote:
What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58


The area of the big square is \((a+b)^2\)

The area of each triangle is \(\frac{ab}{2}\)

Hence, the area of the shaded quadrilateral is
\((a+b)^2-4 \times \frac{ab}{2}=a^2+b^2\)

(1) \(a^2-b^2=40\). We can't know what the value of \(a^2+b^2\) is. Insufficient.

(2) It's clear that \(a^2 + b^2 = 58\) is the area of the shaded quadrilateral . Sufficient.

The answer is B
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Re: What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 13 Mar 2017, 15:15
In order to solve this question, we need to know the lengths of the hypotenuses of the triangles. I think.


What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

Statement (1) gives us two variables, meaning we cannot solve the equation. We cannot extrapolate a hypotenuse length from this equation either. Insufficient.

Statement (2) allows us to determine what the length of side C is by squaring 58. Sufficient.

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Re: What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 15 Mar 2017, 06:24
St 1: a^2-b^2 = 40
or (a+b)(a-b) = 40
number of cases possible. INSUFFICIENT

St 2: a^2 +b^2 = 58.
for each side if the shaded quadrilateral, we can say that a^2 +b^2 = c^2
therefore the shaded region is a square with side c and the area c^2 = 58. ANSWER

Option B

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Re: What is the area of the shaded quadrilateral in the figure above? [#permalink]

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New post 07 Nov 2017, 10:49
Area of the shaded region = Area of square - (sum of all areas of triangles)
\(= (a+b)^2 - 4* [ \frac{1}{2} * a * b]\) ; if you notice area of each triangle is the same \(= \frac{1}{2} *a * b\)
\(= (a+b)^2 - 2ab\)
\(= a^2 + b^2 + 2ab - 2ab\)
\(= a^2 + b^2\)

Statement 1 : Not sufficient.

Statement 2: gives us the direct value of \(a^2 + b^2\)
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Re: What is the area of the shaded quadrilateral in the figure above?   [#permalink] 07 Nov 2017, 10:49
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