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The diagram shows four unit circles and two squares. The gray square is formed by the tangency points between the circles. The blue square is formed by joining the midpoints of each arc that are formed by tangency points.

Find the difference of between the area of the gray square and that of the blue square.

 

 Jan 3, 2021

Best Answer 

 #2
avatar+1162 
+3

The side of a gray square is √2  and its area is square units

 

The area of a blue square         A = 1/2[(√8 -2)2] = 0.34314575

 

The difference between these 2 areas is      1.65685425 square units

 Jan 4, 2021
 #1
avatar+117546 
+2

Side of grey square  = sqrt (2) units

 

Area  of grey square=  (sqrt (2) )^2 =  2

 

 Distance  between  circle drawn  through the diagonal of the  square =  sqrt (8)

 

Diagonal of  blue square =   sqrt (8)  - 2

 

Side of  blue  square =   [ sqrt (8)  - 2 ]  /sqrt (2)

 

Area of blue square = (1/2) (sqrt (8)  -2)^2   = .343

 

Difference  of areas  =   2 - .343 ≈  1.657  units^2

 

 

 

cool cool cool

 Jan 3, 2021
edited by CPhill  Jan 4, 2021
edited by CPhill  Jan 4, 2021
 #2
avatar+1162 
+3
Best Answer

The side of a gray square is √2  and its area is square units

 

The area of a blue square         A = 1/2[(√8 -2)2] = 0.34314575

 

The difference between these 2 areas is      1.65685425 square units

jugoslav  Jan 4, 2021

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