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Math Help - Help needed calculating the area of a rectangle with 2 semi circles on either side

  1. #1
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    Help needed calculating the area of a rectangle with 2 semi circles on either side

    Help needed calculating the area of a rectangle with 2 semi circles on either side-pic20140619163344.jpg

    I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one.

    As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a wall

    Any help or tips would be appreciated
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  2. #2
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    Re: Help needed calculating the area of a rectangle with 2 semi circles on either sid

    Quote Originally Posted by dabeast View Post
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    I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one.

    As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a wall

    Any help or tips would be appreciated
    Specify the length of the rectangle
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  3. #3
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    Re: Help needed calculating the area of a rectangle with 2 semi circles on either sid

    You can use an integral to approximate it, but I don't know if that's the method you'd want to use.

    The radius of the circle is 2.0975 \pm 0.125

    The equation of the circle would be x^2 + y^2 = (2.0975 \pm 0.125)^2

    And so the integral would be:

    \displaystyle \int _{-1.775 \mp 0.125} ^{1.775 \pm 0.125} \sqrt{ (2.0975 \pm 0.125)^2 - x^2 } \, \, dx

    This will give you the area of the left section. Just double it to get the area of the whole thing.
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