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# There is a circle inscribed in a square, shown on the above figure. If

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Math Revolution GMAT Instructor
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There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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23 Feb 2017, 20:28
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4
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35% (medium)

Question Stats:

61% (01:01) correct 39% (00:57) wrong based on 139 sessions

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There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. $$1-π$$
B. $$2-π$$
C. $$4-π$$
D. $$1-(\frac{π}{2})$$
E. $$1-(\frac{π}{4})$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 19 Apr 2016 Posts: 271 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink] ### Show Tags 23 Feb 2017, 20:38 MathRevolution wrote: Attachment: 1.png There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded? A. $$1-π$$ B. $$2-π$$ C. $$4-π$$ D. $$1-(\frac{π}{2})$$ E. $$1-(\frac{π}{4})$$ area of one of the 4 regions shaded = (area of Square - area of circle)/4 = (4-pi)/4 = 1- pi/4 Hence Option E is correct Hit Kudos if you liked it Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7592 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink] ### Show Tags 26 Feb 2017, 21:28 ==> The area of the square-area of the $$circle=2^2- π=4- π$$, and since it asks for one of the 4 regions shaded, you get $$\frac{4- π}{4}=1-(\frac{π}{4})$$. The answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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08 Mar 2017, 22:13
Silly mistake- but fixed it- you have to multiply 1 by 1 to get the area of one fourth of the square and then subtract it by the area of the remaining portion of the circle inside it; though, you can just find the area of the circle and divide it by 4. Thus,

1 x 1= 1
pi (1)^2= pi (1) / 4

1- pi(1)/4
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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09 Mar 2017, 01:20
Side of square = diameter of circle = 2 x radius\therefore radius = diameter/2 = 1

Area of shaded region = area of square - area of circle = 2 x2 - pi*1*1 = 4 -pi

Since there are 4 equal parts of the shaded region, area of one shaded region = (4 -pi)/4 = 1 - pi/4

Option E

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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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29 Jan 2018, 20:23
Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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29 Jan 2018, 21:04
teamryan15 wrote:
Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?

The area is $$pi*r^2$$ itself but the length of square is 2, which is equal to diameter. Hence radius is 2/2=1
So r^2=1^2=1..
What is left is pi*r^2=pi*1^2=pi
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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01 Jun 2019, 23:19
MathRevolution wrote:
Attachment:
1.png

There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. $$1-π$$
B. $$2-π$$
C. $$4-π$$
D. $$1-(\frac{π}{2})$$
E. $$1-(\frac{π}{4})$$

Square Area= 4

Area of circle= PI.

1/4 th of shaded region= (1/4) (4_PI) E
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Re: There is a circle inscribed in a square, shown on the above figure. If   [#permalink] 01 Jun 2019, 23:19
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