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Math Help - Area of a grass field (rectangle + 2 semicircles)

  1. #1
    Member realintegerz's Avatar
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    Area of a grass field (rectangle + 2 semicircles)

    I'm having a hard time with this problem

    A grass field is shaped like a rectangle with semicircles on both ends. The total length of the field is exactly 100 feet. How wide, to the nearest tenth of a foot, should the field be if its total area is 4,000 square feet?


    Can I assume the radius of the circle is 1/2 of the width of the rectangle?

    And I still am not seeing how I could solve this
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    sketch a picture?

    total length of field = length of rectangle + 2 radii

    width of field = 2 radii

    A = \pi r^2 + 2r(100 - 2r)

    you were given A ... solve for r.
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