One arc and two opposite sides form a sector (arcs AC and AB, BC) with an area of π * R squared *90 degrees /360 degrees =4π.

Draw a diagonal. The diagonal line and two sides form a triangle (△ABC), and the square of area = A/2 =8.

The part between diagonal AC and arc AC, area =4π-8.

The shadow area is twice the area between the diagonal and the arc: area =8π- 16.