DeanR

Verified answer

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