Monday, May 19, 2008

Elearn Geometry Problem 76



See complete Problem 76
Area of a Circle, Square, Circular Sector, Lune. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.
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3 comments:

  1. AnonymousJune 18, 2008 at 1:22 PM

    Let the white region have an area W
    Then:

    pi/4 - (S1 + S2 + S3) = W -> (1)

    Which is also equal to Area of circle
    - Area of Blue region

    Area of Circle in center of square of side 1 = pi(0.5)^2 = pi/4

    Therefore W = pi/4 - S -> (2)

    ie. pi/4 -(S1 + S2 + S3) = pi/4 -S

    => S1 + S2 + S3 = S

    ReplyDelete
  2. AnonymousApril 22, 2017 at 7:13 PM

    how to calc the area of S

    ReplyDelete
  3. AnonymousNovember 25, 2018 at 10:19 PM

    Let the white region in the inscribed circle = S4
    and side length of the square = 2x

    S1 + S2 + S3 + S4 = 90/360*π*(2x)^2
    = 1/4*π*4x^2
    = πx^2
    S + S4 = πx^2
    therefore S + S4 = πx^2 = S1 + S2 + S3 + S4
    thus S = S1 + S2 + S3

    ReplyDelete

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