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Math Help - finding the area

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    finding the area

    Find the area of the shaded region

    the radius of each circle is 1

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  2. #2
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    Re: finding the area

    Quote Originally Posted by Mhmh96 View Post
    Find the area of the shaded region

    the radius of each circle is 1
    1. Three of the four midpoints form a right triangle with the length of the hypotenuse of 2. Thus the distance between twoo midpoints placed on a vertical (or horizontal) line is

    d = \sqrt{2}

    2. The triangle formed by a midpoint and two points of interception (marked blue) is a right triangle whose area is

    a = \frac12 \cdot r^2

    3. The lens shaped area is the difference of a quarter circle and the blue right triangle

    l = \frac14 \cdot \pi r^2-\frac12 \cdot r^2 = \frac14 r^2(\pi - 2)

    4. The shaded region's area is the difference of 4 circles and 8 lens shaped areas.
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