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Circumscribing puzzle

Question

If the area of the innermost circle is Pi, what is the area of the red region?

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Red area = Rectangle - 2 triangles.

Inner circle has r=1 (area = pi*r^2=pi). Inner square has length 2, hence diagonally sqrt(2) is the radius of the outer circle, hence the outer square has length 2*sqrt(2).

Rectangle has area (1+sqrt(2))*sqrt(2) = 2 + sqrt(2)

Leftlower triangle has area (sqrt(2))^2/2= 2/2 = 1.

Uppermost triangle has area (sqrt(2)-1)*1/2

Therefore the area of the red triangle is 2+sqrt(2)-1-sqrt(2)/2+1/2=(3+sqrt(2)/2.

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Though your answer makes sense, i am going to hold out a little because i have a slightly different answer.

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araver beat me to it.

Square (1) and two triangles: (1) and {sqrt(2) - 1}/2 = 2.207 ....

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araver beat me to it.

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I found my mistake.  LOL one day, I will be sure to have the answer to my own questions.

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