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# Area of a circumcirlce of equilateral triangle

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Manager
Joined: 16 Apr 2010
Posts: 213

Kudos [?]: 144 [0], given: 12

Area of a circumcirlce of equilateral triangle [#permalink]

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28 Jul 2010, 21:13
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Hi,

The area of an equilateral triangle is 9.what is the area of it circumcircle.

A.10PI
B.12PI
C.14PI
D.16PI
E.18PI

Is this a GMAT question?

regards,
Jack

Kudos [?]: 144 [0], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132696 [1], given: 12335

Re: Area of a circumcirlce of equilateral triangle [#permalink]

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29 Jul 2010, 03:41
1
KUDOS
Expert's post
jakolik wrote:
Hi,

The area of an equilateral triangle is $$9\sqrt{3}$$. What is the area of it circumcircle.

A.10PI
B.12PI
C.14PI
D.16PI
E.18PI

Is this a GMAT question?

regards,
Jack

Edited the stem: it should be "The area of an equilateral triangle is $$9\sqrt{3}$$", (otherwise answer would be $${4\sqrt{3}\pi}$$, which is not listed).

The area of an equilateral triangle equals to $$A=a^2\frac{\sqrt{3}}{4}=9\sqrt{3}$$, where $$a$$ is a side of a triangle --> $$a=6$$.

The radius of the circumscribed circle for equilateral triangle is $$R=a\frac{\sqrt{3}}{3}=2\sqrt{3}$$.

Area of a circle is $$\pi{R^2}=12\pi$$.

Or if you don't remember the formula for radius you should recall another property: radius of a circumscribed circle is 2/3 of the median, which for equilateral triangle is hight too. So calculate height from side and get the radius from it.

For more on this issue please check Triangles Chapter of the Math Book (link in my signature).
_________________

Kudos [?]: 132696 [1], given: 12335

Manager
Joined: 11 Feb 2008
Posts: 89

Kudos [?]: 51 [0], given: 2

Re: Area of a circumcirlce of equilateral triangle [#permalink]

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29 Jul 2010, 03:19
Area=(sqroot3/4)*side^2
9=(sqroot3/4)*side^2
3=(sqroot3/4)*side
side=12/sqroot3

height = (sqroot3/2)*side
= (sqroot3/2)*12/sqroot3
= 6

circumcircle=16*pi

D
_________________

-------------------------------------------------------------------------------------------
Amar
http://amarnaik.wordpress.com

Kudos [?]: 51 [0], given: 2

Manager
Joined: 16 Apr 2010
Posts: 213

Kudos [?]: 144 [0], given: 12

Re: Area of a circumcirlce of equilateral triangle [#permalink]

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29 Jul 2010, 05:01
Thank you again and again for your continues help
Is this a 700+ question?

Kudos [?]: 144 [0], given: 12

Re: Area of a circumcirlce of equilateral triangle   [#permalink] 29 Jul 2010, 05:01
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