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# In the figure above, a circle is inscribed in square WXYZ. What is the

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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06 Jun 2017, 11:27
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15% (low)

Question Stats:

76% (00:58) correct 24% (01:29) wrong based on 102 sessions

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In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:

InscribedWXYZ.png [ 5.38 KiB | Viewed 2867 times ]

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Joined: 30 May 2017
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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06 Jun 2017, 17:36

We just need to figure out the diameter of the circle, as that will be the same length as the side of the square. Once we have these numbers, we can solve for the areas.

Statement one tells us that the diagonal is 4 inches. We can solve for the side length (and therefore the diameter of the circle) by knowing that the diagonal = side length * sqrt(2). Sufficient.

Statement two allows us to solve for radius, which we then double to get the diameter. Since diameter = side length, we can also solve with this info.

Both statements ALONE are sufficient. D
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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06 Sep 2017, 19:50
Bunuel wrote:
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png

You can calculate the area of a square by squaring the diagonal of the square and dividing it by 2.

St 1

This just illustrates the diagonal of wxyz

suff

St 2

From this we can derive the length of the diagonal of wxyz

suff

D
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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02 Nov 2018, 02:26
1
Bunuel wrote:
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png

Dear Moderator,
Please can you check this question, the image for the same is not visible .Thank you.
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- Stne
Math Expert
Joined: 02 Sep 2009
Posts: 58381
Re: In the figure above, a circle is inscribed in square WXYZ. What is the  [#permalink]

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02 Nov 2018, 02:31
stne wrote:
Bunuel wrote:
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

Attachment:
InscribedWXYZ.png

Dear Moderator,
Please can you check this question, the image for the same is not visible .Thank you.

__________________
Fixed that. Thank you.
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Re: In the figure above, a circle is inscribed in square WXYZ. What is the   [#permalink] 02 Nov 2018, 02:31
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