Circular arcs inside a square

Relevant wiki: Circles - Area

Let $x$ be the radius of one quarter circle, then the side length of the square is $2x$ . So we have

$\text{area of the square - area of the yellow region = area of the red region}$

$(2x)^2 - \pi (x^2) = 16(4-\pi)$

$4x^2-x^2 \pi = 16(4-\pi)$

$x^2(4-\pi) =16(4-\pi)$

$x^2=16$

$x=4$

The area of the yellow region is equivalent to the area of a circle of radius $4$ . So the area is $\pi x^2=\boxed{16\pi}$