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A regular octagon is placed in a unit circle such that each vertex lies on the circumference of the circle.

Find the perimeter of the octagon.

 

 Dec 30, 2019
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Using the Law of Cosines, we can find the side of the octagon, S, as

 

S^2  =  1^2 + 1^2   - 2 ( 1 * 1) cos (45°)

 

S^2   = 2  - [ 2 *  √2 / 2 ] 

 

S^2  = 2 - √2

 

S = √ [ 2 - √2 ]    units

 

So....the perimeter is

 

8 √ [ 2  - √2 ] units    ≈  6.12 units

 

 

cool cool cool   

 Dec 30, 2019

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