BMAD Posted August 5, 2015 Report Share Posted August 5, 2015 If the area of the innermost circle is Pi, what is the area of the red region? Quote Link to comment Share on other sites More sharing options...

0 araver Posted August 5, 2015 Report Share Posted August 5, 2015 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)*1/2Therefore the area of the red triangle is 2+sqrt(2)-1-sqrt(2)/2+1/2=(3+sqrt(2)/2. Quote Link to comment Share on other sites More sharing options...

0 BMAD Posted August 6, 2015 Author Report Share Posted August 6, 2015 Though your answer makes sense, i am going to hold out a little because i have a slightly different answer. Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted August 6, 2015 Report Share Posted August 6, 2015 araver beat me to it.Square (1) and two triangles: (1) and {sqrt(2) - 1}/2 = 2.207 .... Quote Link to comment Share on other sites More sharing options...

0 BMAD Posted August 7, 2015 Author Report Share Posted August 7, 2015 araver beat me to it.Hidden Content I found my mistake. LOL one day, I will be sure to have the answer to my own questions. Quote Link to comment Share on other sites More sharing options...

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

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