Results 1 to 2 of 2

Math Help - Radius of Circle

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    134

    Radius of Circle

    The altitude of a triangle is 30 cm and its base is 80 cm. Find the area of the trapezoid formed by a line parallel to the base of the triangle and is 12 cm from the vertex.

    Help please, I really have no idea. Can you show it with illustrations, thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, reiward!

    The altitude of a triangle is 30 cm and its base is 80 cm.
    Find the area of the trapezoid formed by a line
    parallel to the base of the triangle and is 12 cm from the vertex.
    Code:
                    B
      -             *
      :            *| *
      :           * |   *
      :          *  |12   *
      :         *   |       *
     30      D *----+---------* E
      :       *     |           *
      :      *      |             *
      :     *       |18             *
      :    *        |                 *
      - A *---------*-------------------* C
          : - - - - - - 80- - - - - - - :
    The area of a trapezoid is: . A \;=\;\tfrac{h}{2}(b_1+b_2)

    . . where h is the altitude and b_1,b_2 are the lengths of the parallel sides.


    We already know: . h = 18,\;b_1 = 80
    . . We need: . b_2 \,=\,DE

    Since \Delta DBE \sim \Delta ABC\!:\;\;\frac{DE}{12} \,=\,\frac{80}{30} \quad\Rightarrow\quad DE \,=\,32

    Therefore: . A \;=\;\frac{18}{2}(80 + 32) \;=\;1008\text{ cm}^2

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. radius of circle
    Posted in the Geometry Forum
    Replies: 3
    Last Post: June 11th 2010, 09:11 AM
  2. Replies: 7
    Last Post: March 15th 2010, 04:10 PM
  3. Replies: 2
    Last Post: February 6th 2010, 08:31 AM
  4. Radius of Circle #2
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 11th 2009, 05:37 AM
  5. Radius of circle inside a circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 3rd 2009, 11:08 PM

Search Tags


/mathhelpforum @mathhelpforum