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Math Help - Help! Geometry

  1. #1
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    Angry Help! Geometry

    The question is:

    The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

    Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

    Please help!

    Kelli
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  2. #2
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    So you have a circle and a square. I think there has to be more info!
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  3. #3
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    Quote Originally Posted by wynkky View Post
    The question is:

    The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

    Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

    Please help!

    Kelli
    Let us suppose radius of the semicircular ends = r.

    So, side of square = diameter of semicircle = 2r

    Now area of field = Area of two semicircles + Area of square.

    1300 = 2 \times {\frac{\pi r^2}{2}} + (2r)^2

    1300 = \pi r^2 + 4r^2

    1300 = r^2(\pi + 4)

    r^2 = \frac {1300}{\pi + 4}

    r= \sqrt {182.032}

    r= 13.49 yards

    Side of square = 2r = 2 \times 13.49 = 26.98 yards.= 27 yards
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