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Math Help - Pentagon Inscribed In A Circle...

  1. #1
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    Pentagon Inscribed In A Circle...

    Ok. I know how to find the area of, like, a pentagon. But in this problem is wants me to find the area of the courthouse....like outside the pentagon.

    So on a problem like this, do I follow through with steps to find the area of a pentagon and go from there?

    Question:

    The center of the pentagon in VA is a courtyard in the shape of a regular pentagon. The pentagon would be inscribed in a circle with radius of 300 ft. Find the area of the courtyard.



    I drew the pentagon. :]

    What would I do for the next step?
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  2. #2
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    Hi again !
    Quote Originally Posted by topaz192 View Post
    Ok. I know how to find the area of, like, a pentagon. But in this problem is wants me to find the area of the courthouse....like outside the pentagon.

    So on a problem like this, do I follow through with steps to find the area of a pentagon and go from there?

    Question:

    The center of the pentagon in VA is a courtyard in the shape of a regular pentagon. The pentagon would be inscribed in a circle with radius of 300 ft. Find the area of the courtyard.



    I drew the pentagon. :]

    What would I do for the next step?
    The next step will be to change your sketch

    If the pentagon is inscribed in a circle, it means that the circle is all around the pentagon. Here, the circle is inscribed in the pentagon, this is very different !

    Here is a sketch :
    Pentagon Inscribed In A Circle...-600px-regular_pentagon_1.svg.png

    The pentagon is inscribed in the green circle. In order to calculate the area of the pentagon, imagine it can be divided into 5 isosceles triangles (summit is the center).
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  3. #3
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    Whoopsiiee! Lol

    So 360 / 5 = 72 degrees.

    1 / 2 (300?) ^2 sin72 = ____ times 5 sides = ________

    Would that, in any way, lead me to my answer lol
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  4. #4
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    Quote Originally Posted by topaz192 View Post
    Whoopsiiee! Lol

    So 360 / 5 = 72 degrees.

    1 / 2 (300?) ^2 sin72 = ____ times 5 sides = ________

    Would that, in any way, lead me to my answer lol
    YES !!!!
    Multiply the red part by 5 (I didn't quite understand what followed your red part) and you have the result !
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  5. #5
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    Lol i didnt have a calculator near me

    1 / 2 (300?) ^2 sin72 = ANSWER (Times 5)

    I meant like whatever the answer is do it by 5 at the end lol
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  6. #6
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    Lol Thanks [AGAiN!] for your time!!! :]
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