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Math Help - Triangle inscribed in a Hexagon

  1. #1
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    Triangle inscribed in a Hexagon

    Hey sorry if this is in the wrong place and if the picture is too small but I need some help

    What can you say about a triangle that is inscribed in a hexagon, where the vertices of the triangle hits the midpoint of 3 sides of a hexagon?
    if there is something about it please explain it to me so I can understand better, thanks.
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  2. #2
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    Re: Triangle inscribed in a Hexagon

    I don't see a picture...
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    Re: Triangle inscribed in a Hexagon

    sorry i just added it right now
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    Re: Triangle inscribed in a Hexagon

    Is it a regular hexagon or an arbitrary hexagon?
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    Re: Triangle inscribed in a Hexagon

    it is a regular hexagon
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    Re: Triangle inscribed in a Hexagon

    ABCDEF is aregular hexagon. Name the three midpoints that form the triangle
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    Re: Triangle inscribed in a Hexagon

    Hello, gfbrd!

    What can you say about a triangle that is inscribed in a regular hexagon,
    where the vertices of the triangle are the midpoint of 3 sides of a hexagon?

    What do they want me to say?
    . . It has three sides.
    . . It has three angles.
    . . It is equilateral.
    . . It has 60o angles.


    Okay, I'll get serious . . .

    A regular hexagon is composed of six equilateral triangles of side a.
    Consider the upper half of the hexagon.
    Code:
                : - - a - - :
                *  *  *  *  *
               * .         . *
            a *   .       .   * a
             *=================*
            *       .   .       *
           *         . .         *
          *  *  *  *  *  *  *  *  *
          : - - a - - : - - a - - :
    We have an isosceles trapezoid.
    The side of the triangle is the median.
    Its length is the average of the lengths
    . . of the two parallel sides.
    Hence, the side of the triangle is \tfrac{3}{2}a.

    The triangle's perimeter is \tfrac{3}{4} of the hexagon's perimeter.
    The triangle's area is \tfrac{3}{8} of the hexagon's area.
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    Re: Triangle inscribed in a Hexagon

    There are two additional triangles which can be drawn meeting the general requirements
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    Re: Triangle inscribed in a Hexagon

    Great thanks for your help everyone.
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