Hello, Telo!
Draw chord $\displaystyle AK.$Given square ABCD with side $\displaystyle a.$
A and D are centers of quarter-circles.
The arcs intersect at K.
Find the area of shaded region.
Code:B *-*-------*-* C | K*:::::| | */..*:::| | *./.....*:| |*./.......*| a |./.........| */..........* A *-----------* D a
The area of quarter-circle $\displaystyle AKCD$ is:-$\displaystyle \tfrac{1}{4}\pi a^2$
The area of sector $\displaystyle AKD$ is:-$\displaystyle \tfrac{1}{6}\pi a^2$
The area of segment $\displaystyle AK$ is:-$\displaystyle \tfrac{1}{6}\pi a^2 - \tfrac{\sqrt{3}}{4}a^2$
$\displaystyle \text{Shaded region} \:=\:\text{(quarter-circle)} - \text{(sector + segment)}$
. . . . . . . . . . $\displaystyle =\;\tfrac{1}{4}\pi a^2 - \left(\tfrac{1}{6}\pi a^2 + \left[\tfrac{1}{6}\pi a^2 - \tfrac{\sqrt{3}}{4}a^2\right]\right)$
. . . . . . . . . . $\displaystyle =\;\left(\tfrac{\sqrt{3}}{4} - \tfrac{\pi}{12}\right)a^2$