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