Find the area of the shaded region.
The area of the shaded region is

Step 1 ：The area of the outer square is \(4^2 = 16\) square inches.

Step 2 ：The square formed by connecting the midpoints of the outer square has half the area of the outer square, so its area is \(\frac{1}{2} \times 16 = 8\) square inches.

Step 3 ：The smallest square in the diagram is formed by connecting the midpoints of the inner square, so its area is \(\frac{1}{2} \times 8 = 4\) square inches.

Step 4 ：The shaded area is the difference between the area of the inner square and the smallest square, which is \(8 - 4 = 4\) square inches.

Step 5 ：So, the area of the shaded region is \(\boxed{4}\) square inches.