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# What is the area of the shaded region, formed by the

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Senior Manager
Joined: 21 Oct 2013
Posts: 408
What is the area of the shaded region, formed by the  [#permalink]

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20 Jul 2014, 01:53
2
12
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:18) correct 32% (02:47) wrong based on 178 sessions

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What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 - 3π

B. √3 - (4/3)π

C. (3√3)/4

D. √3 - π/3

E. 3√3 - π

Attachment:

Drawing.png [ 14.33 KiB | Viewed 4717 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 61524
What is the area of the shaded region, formed by the  [#permalink]

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20 Jul 2014, 04:43
8
1
goodyear2013 wrote:

What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 -3π
B. √3 - (4/3)π
C. (3√3) / 4
D. √3 - π/3
E. 3√3 - π

You can solve this by process of elimination. The answer should be {area of the triangle} - {area of the circle} = √3 - {something with π}.

A. √3 -3π --> negative. Discard.

B. √3 - (4/3)π --> negative. Discard.

C. (3√3) / 4 --> no π. Discard.

D. √3 - π/3. Keep.

E. 3√3 - π. Greater than √3 (area of the triangle). Discard.

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Joined: 25 Apr 2012
Posts: 642
Location: India
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Re: What is the area of the shaded region, formed by the  [#permalink]

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20 Jul 2014, 04:12
2
1
goodyear2013 wrote:
Attachment:
Drawing.png

What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 -3π
B. √3 - (4/3)π
C. (3√3) / 4
D. √3 - π/3
E. 3√3 - π

Attachment:
Drawing2.png

Is the formula for circle inscribed in the triangle the best way to solve this question?

The question is not as difficult as it looks but under time pressure,chances are you will get it wrong

Area of Eq. Triangle =$$\sqrt{3}$$/4*a^2=$$\sqrt{3}$$ where a is the side of the triangle

Solve for "a" and we get a=2

Now radius of the circle is nothing but the radius of in circle. Radius of in circle for a equilateral triangle is given by
r=$$\sqrt{3}/6$$ *a

or $$r=\frac{1}{\sqrt{3}}$$

Area of the shaded region: Area of Triangle - Area of circle

$$\sqrt{3}$$- π/3

Ans is D
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Joined: 25 Apr 2012
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Location: India
GPA: 3.21
Re: What is the area of the shaded region, formed by the  [#permalink]

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20 Jul 2014, 05:09
Bunuel wrote:
goodyear2013 wrote:
Attachment:
Drawing.png

What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 -3π
B. √3 - (4/3)π
C. (3√3) / 4
D. √3 - π/3
E. 3√3 - π

Attachment:
Drawing2.png

Is the formula for circle inscribed in the triangle the best way to solve this question?

You can solve this by process of elimination. The answer should be {area of the triangle minus} - {area of the circle} = √3 - {something with π}.

A. √3 -3π --> negative. Discard.

B. √3 - (4/3)π --> negative. Discard.

C. (3√3) / 4 --> no π. Discard.

D. √3 - π/3. Keep.

E. 3√3 - π. Greater than √3 (area of the triangle). Discard.

Too Good......

Where was the Math in this ???

FYI, Time to get this answer correct on avg in the thread in 3 min 32 sec...Wonder how much time did you take on this??
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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Math Expert
Joined: 02 Sep 2009
Posts: 61524
Re: What is the area of the shaded region, formed by the  [#permalink]

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20 Jul 2014, 05:30
goodyear2013 wrote:
Attachment:
Drawing.png

What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 -3π
B. √3 - (4/3)π
C. (3√3) / 4
D. √3 - π/3
E. 3√3 - π

Attachment:
Drawing2.png

Is the formula for circle inscribed in the triangle the best way to solve this question?

Check other Shaded Region Problems in our Special Questions Directory.

Hope it helps.
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Re: What is the area of the shaded region, formed by the  [#permalink]

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14 Feb 2019, 00:44
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Re: What is the area of the shaded region, formed by the   [#permalink] 14 Feb 2019, 00:44
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