Results 1 to 5 of 5

Math Help - Right trapeziod area problem

  1. #1
    Newbie
    Joined
    Nov 2008
    From
    Chicago
    Posts
    16

    Right trapeziod area problem

    A right trapezoid has parallel sides AB and CD (AB > CD), a perpendicular side AD. The diagnoal AC equals to the side AB and the side AD equals to the side DC. A line through C, perpendicular to side BC intersects side AD in the point F. Find the area of the trapezoid if we know that DF=1.

    Can someone please tell me how to set this problem up? I can solve it from there...

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    \widehat{ACD}=\widehat{CAD}=\frac{\pi}{4}

    Let \widehat{ACB}=\widehat{ABC}=x. Then 2x+\frac{\pi}{4}=\pi\Rightarrow x=\frac{3\pi}{8}

    \widehat{FCA}=\frac{\pi}{2}-x=\frac{\pi}{2}-\frac{3\pi}{8}=\frac{\pi}{8}

    Then \widehat{DCF}=\frac{\pi}{4}-\frac{\pi}{8}=\frac{\pi}{8}.

    In the triangle CDF: \tan\frac{\pi}{8}=\frac{DF}{CD}=\frac{1}{CD}

    Then CD=\frac{1}{\tan\frac{\pi}{8}}=\cot\frac{\pi}{8}=\  sqrt{\frac{1+\cos\frac{\pi}{4}}{1-\cos\frac{\pi}{4}}}=\sqrt{2}+1=AD.

    AB=AC=AD\sqrt{2}=2+\sqrt{2}

    Now you have all the elements to find the area.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Let's see if I can make this clear enough for you . . .

    WE DON'T DO YOUR HOMEWORK!

    If you can't show a little initiative on your part,
    show some work, evidence of some effort,
    STOP WASTING OUR TIME!


    Mod: Is THAT the message I should give all visitors?
    .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2008
    From
    Chicago
    Posts
    16

    not homework

    This is not for homework. I am doing this problem for fun. Thanks.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2008
    From
    Chicago
    Posts
    16
    Thanks, red_dog. I wasn't sure whether or not I was correct in using tan...I am out of practice.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area Problem
    Posted in the Geometry Forum
    Replies: 6
    Last Post: August 25th 2010, 01:51 PM
  2. Differential eq problem and area problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 5th 2009, 04:46 PM
  3. Replies: 4
    Last Post: December 16th 2008, 10:45 PM
  4. Area - Problem Sum
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 4th 2007, 09:47 AM
  5. problem with area
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: October 12th 2007, 11:01 AM

Search Tags


/mathhelpforum @mathhelpforum