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Four diagonals of a regular octagon with side length 2 intersect as shown. Find the area of the shaded region.

michaelcai  Aug 25, 2017
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The triangle just to the left of the blue area is a 45-45-90 triangle....and the side opposite the 90° angle has a length of  2√2 units  = √8  units

 

And  the blue area is a parallelogram with equal sides of this length

 

And the acute angle in the parallelogram = 45°

 

So....its area  =

 

2 * (1/2) (√8)^2 sin (45°)  =

 

8 / √2   units^2   =  8 √2 / 2  units^2  = 4 √2  units^2

 

 

cool cool cool

CPhill  Aug 25, 2017

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