Squares & Star

Overall area = $(2 + \sqrt{2} )^2 + 4 (\frac{1}{2}) = 8 + 4 \sqrt{2}$

Subtract the area of the 8 yellow squares, we get the area of the blue star as $4 \sqrt{2} = 5.657$

The side length of each big square is $2+\sqrt 2$ units. The total area of the outer star shaped region is $(2+\sqrt 2)^2+4\times \dfrac{1}{2}=8+4\sqrt 2$ square units. The total area of the eight yellow squares is $8\times 1=8$ square units. Hence the area of the inner star is $8+4\sqrt 2-8=4\sqrt 2\approx \boxed {5.657}$ square units.