Four quarter circles of radius 1, each containing a square. What is the blue area?

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The blue area is √3/2.

Draw the radius to the square vertex a shown. It forms a blue right triangle with short side 1/2 and hypotenuse 1. The angle at the centre therefore is 60°. The large blue triangles area double that and so the total blue area is 2*1/2*1*1*sin(120°)=√3/2.

Visual solution

Solution without words by David Andriana.


The butterfly
They taught him how to fly
They flutter and put sparkle in your eye
They fly and give you a smile
Changing from chrysalis into butterfly
The butterfly will appear
To be nice for all you dear
Just a sign of endurance
Against intolerance
And join for a new chance


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