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# In the figure to the BELOW, QRST is a square. If the shaded region is

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SVP
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 1738
Location: Pakistan
GPA: 3.39
In the figure to the BELOW, QRST is a square. If the shaded region is  [#permalink]

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18 May 2017, 13:47
1
1
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:19) correct 11% (02:11) wrong based on 29 sessions

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In the figure to the below, QRST is a square. If the shaded region is bounded by arcs of circles with centers at Q, R, S, and T, then the area of the shaded region is

(A) 9
(B) 36
(C) 36 – 9π
(D) 36 – π
(E) 9 – 3π

Source: Nova GMAT

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Joined: 21 Jan 2017
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Re: In the figure to the BELOW, QRST is a square. If the shaded region is  [#permalink]

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18 May 2017, 14:21
Length of Side of Square RSTQ= 3+3=6 units
Hence, Area of Square RSTQ= 36 units sq.

Radius of each circle= 3 units
Area of unshaded white portion= π(3)^2=9π

Area of shaded part= Area of square- Area of unshaded part= 36-9π

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Concentration: Finance, Accounting
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Re: In the figure to the BELOW, QRST is a square. If the shaded region is  [#permalink]

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19 May 2017, 01:06
Length of side of square= 3+3= 6 units
Area of Square= $$(Side)^2$$= $$(6)^2$$= 36 units
Area of 1 sector of a circle= $$\frac{90}{360}$$*$$\pi$$$$r^2$$
Area of 4 sector of a circle= Area of a complete circle= $$\pi$$$$r^2$$= 9$$\pi$$
Area of Shaded region= Area of square- Area of 4 sector of a circle
= 36-9$$\pi$$

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Re: In the figure to the BELOW, QRST is a square. If the shaded region is &nbs [#permalink] 19 May 2017, 01:06
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