Do these areas have any special meaning or name?

Question

I was just toying around with circles and squares.

Do the red areas in the picture have any special meaning somehow?

Answer 1

If you take both circles of same radius r, then you can compare the areas of red parts in both figures:
In fig 1: $$A(square)=(2r)^2=4r^2$$ $$A(circle)=\pi r^2$$

$$A(red part)=4r^2-\pi r^2 =(4-\pi)r^2$$

In fig 2:
$$A(circle)=\pi r^2$$ diagonal of square=2r, its side will be $r \sqrt 2$ $$A(square)={(r \sqrt 2}^2)=2r^2$$

$$A(red part)=\pi r^2-2r^2=(\pi -2)r^2$$

So, as such there's no definite relation or special meaning between their areas.
Name you ask, may be there's none specifically.