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

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

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New post 18 May 2017, 12:47
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Difficulty:

  25% (medium)

Question Stats:

81% (01:01) correct 19% (01:10) wrong based on 27 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
[Reveal] Spoiler: OA

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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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New post 18 May 2017, 13:21
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

Answer=C
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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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New post 19 May 2017, 00:06
Length of side of square= 3+3= 6 units
Area of Square= \((Side)^2\)= \((6)^2\)= 36 units
Radius of circle= 3 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\(\pi\)

Answer: C.

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Re: In the figure to the BELOW, QRST is a square. If the shaded region is   [#permalink] 19 May 2017, 00:06
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In the figure to the BELOW, QRST is a square. If the shaded region is

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