Let the radius of the big circle be r and the radius of the small circle be r, then the area of the big square is r? The area of the small square is r? The area of the great circle is πR? , the area of the small circle is πr? .

Shadow area = large square area-small square area =R? -r？ =90? .

Ring area = large circle area-small circle area =πR? -πr？ =π(R？ -r？ )=90π? ≈282.74? .