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In the figure above, vertex R of square PQRS is the center of the circ

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Joined: 02 Sep 2009
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In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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16 Nov 2017, 22:57
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In the figure above, vertex R of square PQRS is the center of the circle. If QT = TR = 3, what is the area of the shaded region?

(A) 9 + 27π/4
(B) 9 + 27π
(C) 36 + 27π/4
(D) 36 + 9π
(E) 36 + 27π

[Reveal] Spoiler:
Attachment:

2017-11-17_0948.png [ 6.48 KiB | Viewed 633 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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17 Nov 2017, 00:35
Area of shaded region = Area of square + 3/4 Area of the circle = 6^2+3/4*P*3^2=36 + 27/4*P
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Re: In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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17 Nov 2017, 09:09
Bunuel wrote:

In the figure above, vertex R of square PQRS is the center of the circle. If QT = TR = 3, what is the area of the shaded region?

(A) 9 + 27π/4
(B) 9 + 27π
(C) 36 + 27π/4
(D) 36 + 9π
(E) 36 + 27π

[Reveal] Spoiler:
Attachment:
2017-11-17_0948.png

Area of square is 6^2 = 36
Area of 3/4 th Circle is $$\frac{3π3^2}{4}$$ = $$\frac{27π}{4}$$

So, Area of the total figure is $$36$$ + $$\frac{27π}{4}$$, answer will be (C)
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Re: In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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18 Nov 2017, 02:12
As the length of both QT and TR are equal. So we can deduce that the length of the side of the Square is 6 and radius of the circle is 3. From this we can find the areas of the square and the Circle and add both.
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Re: In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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19 Nov 2017, 03:12
Side of Square = QT+TR =3+3 =6
Area Square = 6*6 =36
Area of 3/4 Circle = 3/4 * pie *3*3= pi*27/4
Total area 36+ pi*27/4, Answer = C
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Re: In the figure above, vertex R of square PQRS is the center of the circ [#permalink]

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20 Nov 2017, 12:25
Bunuel wrote:

In the figure above, vertex R of square PQRS is the center of the circle. If QT = TR = 3, what is the area of the shaded region?

(A) 9 + 27π/4
(B) 9 + 27π
(C) 36 + 27π/4
(D) 36 + 9π
(E) 36 + 27π

[Reveal] Spoiler:
Attachment:
2017-11-17_0948.png

We can consider the shaded region as the total area of a square and ¾ the area of a circle.

Since TR = 3, the radius of the circle is 3 and the side of the square is 6.

Thus:

Area of the square is 6 x 6 = 36.

3/4 of the area of the circle is 3/4 x π x 3^2 = 27π/4.

So, the area of the shaded region is 36 + 27π/4.

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Re: In the figure above, vertex R of square PQRS is the center of the circ   [#permalink] 20 Nov 2017, 12:25
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