We have a square of side 20, area 400
Inscribed in that square is a circle of diameter 20, radius 10, area 100π
Inscribed in the circle is a square with diagonal 20, so side 20/√2, so area (20/√2)²=200.
So the outer shaded ring is area 100π - 200.
So far so good.
The area of the inner shaded diamond is the large square less four quarter circles of radius 10. That's 400 - 100π.
So our total shaded area is (100π - 200) + (400 - 100π)
Answer: 200 square units
