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Math Help - Geometry: Urgent Help: Area of Trapezoid Circum. Abt Circle

  1. #1
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    Geometry: Urgent Help: Area of Trapezoid Circum. Abt Circle

    Hiii, this is a problem that I have encountered and I need help ASAP.
    This is the figure:

    Thanks a lot!!
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  2. #2
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    Quote Originally Posted by Yumi
    Hiii, this is a problem that I have encountered and I need help ASAP.
    This is the figure:

    Thanks a lot!!
    Hello,

    I've attached a diagram to demonstrate what I calculated.

    Let r be the radius of the circle.

    Let angle(CBA)= alpha. Then angle(DCB)=180-alpha.

    The triangle (BMO) is a right triangle. The triangle (OSC) is a right triangle.

    Now use the tangens:

    \frac{r}{9}=\tan \left( \frac{\alpha}{2}}\right)

    \frac{r}{4}=\tan \left(90^\circ- \frac{\alpha}{2}}\right)

    with \tan \left(90^\circ- \frac{\alpha}{2}} \right) =\frac{1}{\tan \left( \frac{\alpha}{2}}\right) }

    So you get:

    \frac{r}{9}=\frac{1}{ \frac{r}{4}}

    Solve for r and you'll get r = 6.

    That means the height of the trapezoid is 12. Therefore the area is 156 (square units).

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Geometry: Urgent Help: Area of Trapezoid Circum. Abt Circle-trap_umkreis.gif  
    Last edited by earboth; April 9th 2006 at 12:17 AM. Reason: mistake in spelling
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  3. #3
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    There is something easier which you can do. If I remember correctly the height of a trapezoid where a circle can be inscribed is the geometric mean of its bases.
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  4. #4
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    I see! Thank you so much for the detailed responses and thanks to ThePerfectHacker also Both gets to the same answer Once again, thank you so much!
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