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Math Help - Ratios of Area in Rectangles

  1. #1
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    Ratios of Area in Rectangles

    These two problems are giving me a lot of trouble. If any one could give me some help in the right direction I'd really appreciate it.

    1 In rectangle ABCD, point E is on side AB so that AE = 10 and EB = 5. What fraction of the area of the rectangle is inside triangle AEC?

    2 M and N are the midpoints of consecutive sides of a square ABCD with vertex A in between M and N. What is the ratio of the area of triangle AMN to the area of the complete square.

    Thanks again.
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  2. #2
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    Quote Originally Posted by lyyy94 View Post
    These two problems are giving me a lot of trouble. If any one could give me some help in the right direction I'd really appreciate it.

    1 In rectangle ABCD, point E is on side AB so that AE = 10 and EB = 5. What fraction of the area of the rectangle is inside triangle AEC?

    2 M and N are the midpoints of consecutive sides of a square ABCD with vertex A in between M and N. What is the ratio of the area of triangle AMN to the area of the complete square.

    Thanks again.
    1) Area of ABCD = AB*BC
    Area of AEC = 1/2*AE*BC
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  3. #3
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    Hello, lyyy94!

    1. In rectangle ABCD, point E is on side AB so that: . AE = 10,\;\;EB = 5
    What fraction of the area of the rectangle is inside triangle AEC?
    Code:
          :      10       E   5   :
        A o - - - - - - - o - - - o B
          |  *:::::::::::::*      |
          |     *:::::::::::*     |
          |        *:::::::::*    |
        x |           *:::::::*   | x
          |              *:::::*  |
          |                 *:::* |
          |                    *:*|
        D o - - - - - - - - - - - o C
                     15
    The length of the rectangle is 15.
    The width of the rectangle is x.

    The area of \Delta AEC\:=\:\tfrac{1}{2}(10)(x) \:=\:5x
    The area of rectangle ABCD \:=\:15x

    The fraction (ratio) is: . \frac{5x}{15x} \;=\;\frac{1}{3}





    2. M and N are midpoints of sides DA and AB of square ABCD.
    What is the ratio of the area of \Delta AMN to the area of the square?
    Make a sketch and the answer is obvious . . .
    Code:
                  N
        A o - - - o - - - o B 
          |:::::* | *     |
          |:::*   |   *   |
          |:*     |     * |
        M o - - - + - - - *
          | *     |     * |
          |   *   |   *   |
          |     * | *     |
        D o - - - * - - - o C
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