Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the complete problem 692.
Wednesday, November 23, 2011
Problem 692: Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya
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side of the square : 4r
ReplyDeletetotal 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
Let OE = 1
ReplyDeleteEF = 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