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

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## Solution

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

## Poem

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