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

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What is the area of the shaded region, formed by the [#permalink]

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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

[Reveal] Spoiler:
Attachment:
Drawing.png
Drawing.png [ 14.33 KiB | Viewed 2207 times ]
[Reveal] Spoiler: OA

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

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New post 20 Jul 2014, 05:12
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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

[Reveal] Spoiler:
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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What is the area of the shaded region, formed by the [#permalink]

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goodyear2013 wrote:
Image

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.

Answer: D.
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Re: What is the area of the shaded region, formed by the [#permalink]

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New post 20 Jul 2014, 06:09
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

[Reveal] Spoiler:
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.

Answer: D.


Too Good...... :clap: :clap:

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

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New post 20 Jul 2014, 06:30
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

[Reveal] Spoiler:
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: What is the area of the shaded region, formed by the   [#permalink] 03 Oct 2017, 10:39
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