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Eight identical circles, each of radius one unit are arranged in a blue rectangle as shown. What is the area of the blue rectangle?

 

 Jan 10, 2020
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The base is easy.....it's just 6 units

 

And  if we join  the  center of the  top circle with the  centers of the  two middle circles we will have an equilateral triangle with sides of  2r

 

And the  height, h, of  one of these triangles can be found as

 

tan 60°   =   h 

 

√3  = h

 

So....by symmetry.....the  height of this rectangle  =  2  + 2√3

 

So....its area = 

 

6  (2 + 2√3)  =

 

12 + 12√3  =

 

12 ( 1 + √3)  units^2 ≈   32.78 units^2

 

 

cool cool cool

 Jan 10, 2020

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