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Math Help - Find the Area of a Portion of a Square

  1. #1
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    Find the Area of a Portion of a Square

    Dear Sir,
    I appreaciate very much if someone can help me in the below question.
    Thanks



    ABCD is a square. AFC and BFE are straight lines. Given AE = ED. Find the shaded area of the square.
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  2. #2
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    re: Find the Area of a Portion of a Square

    EBA is 0.25 ABCD and ABC is 0.5 ABCD does that help?
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  3. #3
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    re: Find the Area of a Portion of a Square

    To use reply #2, you must know that triangles \Delta EFA~\&~\Delta CFB are similar.
    So the area of \Delta EFA is one-forth the area of \Delta CFB
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  4. #4
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    re: Find the Area of a Portion of a Square

    I am aware that fact and also ABC is 0.5 of ABCD but got stuck from here on.
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  5. #5
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    re: Find the Area of a Portion of a Square

    Yes I know it can be done using Similar Traingles facts but I wonder how it can be done by a simpler approach. This is what required in this question for students who have not studied similar triangles.
    thanks
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  6. #6
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    re: Find the Area of a Portion of a Square

    Hi kingman,
    Draw a line fromE parallel to AB meeting AC @ G. The area you seek consists of one squareand 1/2 square side lengths a/2 plus triangle EFG where a is length of large square side.Your problem is then to find the altitude of EFG
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