Inside seven squares

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Problem



Seven squares are set inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.

 

Image
Inside Seven Squares



The centre square has the area of $1$ (one) square unit.

What is the total area of the four outside triangles which are outlined in red?

This problem is also available in French: Les 7 carrĂ©s

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