Each of the arcs are in quarter circles. Find the area of the shaded

Take the bigger square ABCD with side 5.
Total area = 5*5=25
Area of sector ABYD=\(\frac{1}{4}*A(circle \ \ with \ \ radius \ \ 5)=\frac{1}{4}*\pi * r^2=\frac{1}{4}*\pi * 5^2=\frac{25\pi }{4}\)
Similarly Area of sector CDXB = \(\frac{25\pi }{4}\)
The area of DXBY =\(A_{(ABYD)}+A_{(CDXB)}- A_{(ABCD)}=\frac{25\pi }{4}+\frac{25\pi }{4}-25=25(\frac{\pi }{2}-1)\)

Now, take the smaller square with side 3 as shown by brown lines.
Total area = 3*3=9
Area of sector EGQB=\(\frac{1}{4}*A(circle \ \ with \ \ radius \ \ 3)=\frac{1}{4}*\pi * r^2=\frac{1}{4}*\pi * 3^2=\frac{9\pi }{4}\)
Similarly Area of sector FGPB = \(\frac{9\pi }{4}\)
The area of GPBQ =\(A_{(EGQB)}+A_{(FGPB)}- A_{(EBFG)}=\frac{9\pi }{4}+\frac{9\pi }{4}-9=9(\frac{\pi }{2}-1)=\)

Area of the shaded portion = area of DXBY - area of GPBQ = \(25(\frac{\pi }{2}-1)-9(\frac{\pi }{2}-1)=16(\frac{\pi }{2}-1)=8\pi -16\)

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