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What fraction of the regular octagon is shaded blue?

 

 Jan 23, 2021
 #1
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Call the side of the  octagon, S

 

Area of  octagon  = 2(1 + sqrt (2) ) S^2

 

Blue  area  = 2 (1/2)  (S/sqrt2)^2    +  (S/sqrt (2))*S  = 

 

S^2 / 2 +  S^2 / sqrt (2)   =

 

( 1/2 + 1/sqrt (2)) S^2  =

 

(1/2)  ( 1 + sqrt (2) ) S^2

 

Blue Area  / Total Area =    (1/2)  / (2)   = 1/4

 

 

cool cool cool

 Jan 23, 2021

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