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Thread: 650 + questions geometry

  1. #1
    Eager! freezer just joined TestMagic.
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    650 + questions geometry

    The area of an equilateral triangle is 9.what is the area of it circumcircle.
    A.10
    π
    B.12π
    C.14π
    D.16π
    E.18π



    Could anybody give me a step by step solution?

    Thanks

  2. #2
    Within my grasp! ken_english is on the way! ken_english's Avatar
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    is it 10 pi

  3. #3
    Within my grasp! tublai is on the way!
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    "a" = length of a side of equilateral triangle

    sqrt(3) / 4 * a^2 = 9 as per the question stem

    => a^2 = 12 * sqrt(3)

    Radius of circumcricle of an equilateral triangle ( this is special case ) = a / sqrt(3)

    => R = a / sqrt(3)

    => R^2 = a^2 / 3 = 4 * sqrt(3)

    Area of circumcircle = pi * R^2 = pi * 4 * sqrt(3)


    I am not getting any of the above answer choices..Not sure where I am going wrong..
    Last edited by tublai; 10-18-2007 at 02:17 AM.

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    Trying to make mom and pop proud notsofast just joined TestMagic.
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    Ken English can you explain your answer?

    Tublai I don't get it at all. What does "a" mean? If "a" is area of the triangle we're given that.

    I'm sorry but both of these are totally unhelpful.

  5. #5
    Within my grasp! tublai is on the way!
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    Quote Originally Posted by notsofast View Post
    Ken English can you explain your answer?

    Tublai I don't get it at all. What does "a" mean? If "a" is area of the triangle we're given that.

    I'm sorry but both of these are totally unhelpful.
    I'm sorry notsofast..I forgot to mention what is "a"

    a = side of equilateral triangle, then area of that equilateral triangle is sqrt(3) / 4 * a^2

    I have edited my earlier post..

  6. #6
    Eager! Protagonist just joined TestMagic.
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    My answer is 4*rt3*pi

  7. #7
    Eager! Protagonist just joined TestMagic.
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    Here are some Equilateral Triangle properties :

    For an
    Equilateral Triangle with side 'a':

    Circumscribed Circle Radius

    Inscribed Circle Radius

    Area


    Perimeter


    Altitude


    Median

  8. #8
    Eager! samdamn just joined TestMagic.
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    answer is 4 pi sqrt 3

  9. #9
    Eager! samdamn just joined TestMagic.
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    you can solve it even if you dont know the formulaes

    lets assume radius is r; side is a; ht is h

    we can form the equations to arrive at the solution...

    let me see if I can draw something and attach it here

  10. #10
    Eager! Protagonist just joined TestMagic.
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    yes you are right, all the above formulae can be derived easily

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