Let radius of half circles be r where 4r=4 given then r=1

area of half petal=

difference between area of sector-area of triangle in context with quarter sector

=\pir^{2}/4-r^{2}/2=r^{2}(\pi-2)/4

8 such half petals=(8)(r^{2}(\pi-2)/4)=2r^2(\pi-2) equation 1

area of inside square with side 2r=(2r)(2r)=4r^2   equation 2

area between inside square and half circles in 8 parts=

diffrence as r^2/2-r^2/4(\pi-2)

8 such parts accumulates area=(8)[r^2/2-r^2/4(\pi-2)]=2r^2(4-\pi) equation 3

adding all area from equation 1 2 and 3= required non shaded part=

8r^2=(8)(1)^2=8.