Is there a way to calculate the area of this intersection of four disks without using an integral? Is there anyway to calculate this area without using integral ?


$$\begin{align}
\text{Let $r$ be radius of circle in square, $if$}\\
\text{ $r$} &= 10\\
\text{by coordinate geometry marked Area}
&= \left( \frac {\pi + 3 - 3 \sqrt 3}{3} \right) \cdot r^2\\
&\approx 31.51
\end{align}$$
