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Thread: area ratio in a parallelogram

  1. #1
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    area ratio in a parallelogram

    Hello,

    My first post in this forum and hi everyone... I need a little help with the following geometry question, it should not be so difficult but i stumbled....

    The shape in the attached is a parallelogram
    the points L,K,F,E are at the mid points of the sides of the parallelogram
    The shaded area is 16 cm2

    what is the area of the whole parallelogram ABCD?
    Attached Thumbnails Attached Thumbnails area ratio in a parallelogram-20181015_160116-copy.jpg  
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  2. #2
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    Re: area ratio in a parallelogram

    Quote Originally Posted by ketanco View Post
    My first post in this forum and hi everyone... I need a little help with the following geometry question, it should not be so difficult but i stumbled....
    The shape in the attached is a parallelogram
    the points L,K,F,E are at the mid points of the sides of the parallelogram
    The shaded area is 16 cm2 , what is the area of the whole parallelogram ABCD?
    If you show us what work that you have done on this problem then we will know how to help you to continue.
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  3. #3
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    Re: area ratio in a parallelogram

    Quote Originally Posted by ketanco View Post
    The shaded area is 16 cm2
    what is the area of the whole parallelogram ABCD?
    >16 cm2
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  4. #4
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    Re: area ratio in a parallelogram

    Here's a hint on how to approach this: since the problem doesn't state the angles of the corners, you can pick whatever angles you want. Similarly, the problem doesn't state the lengths of the sides of the parallelogram, so again you can pick whatever values you want. Therefore you can solve the problem using a square rather than a parallelogram. Try it and see if this simplifies things.
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    Re: area ratio in a parallelogram

    Quote Originally Posted by DenisB View Post
    >16 cm2
    thanks ! helpful...
    Last edited by ketanco; Oct 18th 2018 at 01:58 AM.
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  6. #6
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    Re: area ratio in a parallelogram

    Quote Originally Posted by Plato View Post
    If you show us what work that you have done on this problem then we will know how to help you to continue.
    ok
    i didn't know about it

    i marked ratios of sides of triangles inside. so the ratio area of triangles are 1 at the top to 3 at the bottom each. but i just can not relate ratio of the parallelogram in the middle to triangles on the sides
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