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Math Help - Geometry Similarity

  1. #1
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    Geometry Similarity

    Can you please help me with this and show me where to go? Me and my family have no idea where to start

    ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallelograpm ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

    Thanks

    Michael and family
    Last edited by maltaman; May 11th 2008 at 03:07 AM. Reason: I forgot to thank the person who will answer my question
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  2. #2
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    Quote Originally Posted by maltaman View Post
    Can you please help me with this and show me where to go? Me and my family have no idea where to start

    ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallelograpm ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

    Thanks

    Michael and family
    Call the length of side AD x and the length of AB y.

    Then FG = x/4.

    Now, the area of the parallelogram is given by
    A = xy~sin(\theta)
    where \theta is the angle between AB and AD.

    Now, BCGF is a trapezoid with bases BC and FG parallel. So it's area will be
    a = \frac{1}{2} \left ( x + \frac{x}{4} \right ) y~sin(\theta)

    Can you fill in the missing steps in my derivation and can you take it from here?

    -Dan
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