The four interior circles are equal. Look at the bounded areas 1 and 2.which is large?

Area of the large circle is : $\pi R^2 = \pi ( 2 r )^2 = 4r^2 \pi$

Area of one small circle : $\pi r^2 \implies \text { area of 4 small circles } = 4 r^2 \pi$

$\implies$ Area of large circle = Area of $4$ small circles.

Thus, the area of one blue region = $4 \pi r^2 - 4 \pi r^2$ + area one red region $\implies$

One red region = One blue region ( according to areas )

I started by supposing that the radius of the smaller circles was 1 for simplicity, the rest followed

Each region has an area of $\dfrac{π-2}{2}$ square units considering the radius of the big circle to be $2$ units.