Wednesday, November 23, 2011

Problem 692: Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 692.

Online Geometry Problem 692: Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya.
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2 comments:

  1. AnonymousNovember 24, 2011 at 7:42 AM

    side of the square : 4r

    total area of 4 small circle
    4*(pi*r^2)=4(A+yellow)

    are of big circle
    4*pi*r^2=4(A+blue)

    blue=yellow

    ReplyDelete
  2. PravinNovember 26, 2011 at 5:40 AM

    Let OE = 1
    EF = OB = √2
    Area of yellow shaded area (square) = 2
    Area of outer square = 4
    Area of inner circle = π
    Area of outer circle = 2π
    Area of torus = 2π - π = π
    Area of outer white = (2 π - 4)/2 = π - 2
    Area of blue shaded area = π - (π - 2) = 2
    We are done

    ReplyDelete

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