Draw a diagonal line from the upper left corner to the lower right corner, and you can divide the shadow into two parts equally.

First, only half the area is calculated, that is, 1/4 circle area minus triangle area.

=( 1/4)π(4^2)-( 1/2)(4^2)

So the shaded part

=2[( 1/4)π(4^2)-( 1/2)(4^2)]

=( 1/2)π(4^2)-(4^2)

=(π/2- 1)(4^2)

=8π- 16

=9. 12