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Math Help - area of trapezoid

  1. #1
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    area of trapezoid

    ABCD is a square with area 16 sq meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC?

    A) 8 sq units B) 10 sq units C) 6 sq units D) 16 sq units
    E) 12 sq units
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  2. #2
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    Quote Originally Posted by sri340 View Post
    ABCD is a square with area 16 sq meters. E and F are midpoints of sides AB and BC, respectively. What is the area of trapezoid AEFC?

    A) 8 sq units B) 10 sq units C) 6 sq units D) 16 sq units
    E) 12 sq units
    Hint: The two parallel sides have lengths of 2m and 4m respectively (why?) and the height is 4m (why?).
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  3. #3
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    Hello, sri340!

    Did you make a sketch?


    ABCD is a square with area 16 mē.
    E and F are midpoints of sides AB and BC, respectively.
    What is the area of trapezoid AEFC ?

    . . A) 8 mē . . B) 10 mē . . C) 6 mē . . D) 16 mē . . E) 12 mē
    Code:
                  E
        A *-------*-------* B
          | *:::::|:*     |
          |   *:::|:::*   |
          |     *:|:::::* |
          * - - - *:-:-:-:* F
          | *     | *:::::|
          |   *   |   *:::|
          |     * |     *:|
        D *-------*-------* C

    With a few lines, we see that the square
    . . is divided into 8 congruent right triangles.
    The trapezoid occupies 3 of these triangles.

    Therefore . . .

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