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Area of a circumcirlce of equilateral triangle

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Area of a circumcirlce of equilateral triangle [#permalink]

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New post 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

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Joined: 02 Sep 2009
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Re: Area of a circumcirlce of equilateral triangle [#permalink]

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New post 29 Jul 2010, 03:41
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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 \(\pi{R^2}=12\pi\).

Answer: B.

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

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New post 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

Circumradius= 2/3*height=4
circumcircle=16*pi

D
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Amar
http://amarnaik.wordpress.com

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

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

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New post 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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Area of a circumcirlce of equilateral triangle

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