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math

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I am supposed to find the area of a segment of a circle. The circle is cut with two radi with an angle of 90 degrees. Then where the radi touch the circle another line is drawn to connect them. The triangle and the small section between the triangle and the edge of the circle are the shaded areas. It also tells me that the unshaded area of the circle is 3 m

  • math -

    If the area of the unshaded region in your diagram is 3 m^2, then the whole circle must be 4 m^2 (simple ratio)
    and the area of the sector, which is your shaded region, must be 1 m^2

    so πr^2 = 4
    r^2 = 4/π
    r = 2/√π

    area of your triangle within your shaded region
    = (1/2)r^2
    = (1/2)4/π = 2/π

    area of segment = 1 - 2/π or (π - 2)/π

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