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Math Help - octagon

  1. #1
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    octagon

    Hello everyone, I do not know if I am solving this problem well,

    perhaps not so simple as I see it:

    Two octagons equal have a common side. Find the angle between the sides of both polygons consecutive common.Find the area of the figure if the side is 2m.


    I draw on the figure I made:



    And according to the following theory:

    In a regular octagon, with sides and angles that are equal, the sides are joined at an angle of 135 degrees or \displaystyle\frac{3\pi}{4} rad. Each outer corner of the regular octagon is 45 or \displaystyle\frac{\pi}{4}  rad.

    And so I think then that the sum 45 + 45 = 90 degrees to the exterior angle formed by the two side keys names to common.


    Furthermore, the area of an octagon side t is:

    A = 2t^2(1 + \sqrt[ ]{2})

    I am well on these considerations?

    A greeting and thank you very much
    Attached Thumbnails Attached Thumbnails octagon-octagon.jpg  
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  2. #2
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    Hello, Dogod11!

    You're right on both counts!

    That exterior angle is 90.

    And your area formula is correct.

    Good work!

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  3. #3
    Junior Member
    Joined
    May 2009
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    Quote Originally Posted by Dogod11 View Post
    Hello everyone, I do not know if I am solving this problem well,

    perhaps not so simple as I see it:

    Two octagons equal have a common side. Find the angle between the sides of both polygons consecutive common.Find the area of the figure if the side is 2m.


    I draw on the figure I made:



    And according to the following theory:

    In a regular octagon, with sides and angles that are equal, the sides are joined at an angle of 135 degrees or \displaystyle\frac{3\pi}{4} rad. Each outer corner of the regular octagon is 45 or \displaystyle\frac{\pi}{4}  rad.

    And so I think then that the sum 45 + 45 = 90 degrees to the exterior angle formed by the two side keys names to common.


    Furthermore, the area of an octagon side t is:

    A = 2t^2(1 + \sqrt[ ]{2})

    I am well on these considerations?

    A greeting and thank you very much




    Is correct!!The area if the octagon have to be right!
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  4. #4
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    Thanks!!
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  5. #5
    EX5
    EX5 is offline
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    Nice

    I found no fault in your calculations, good job.
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