1. **Problem statement:** Given a square ABCD with side length 8, a smaller square is formed by joining the midpoints of each side of ABCD. We need to find the perimeter of this smaller shaded square. 2. **Formula and rules:** When the midpoints of a square are joined, the resulting figure is another square whose side length is $\frac{\sqrt{2}}{2}$ times the side length of the original square. 3. **Calculate the side length of the smaller square:** $$\text{Side of smaller square} = 8 \times \frac{\sqrt{2}}{2} = 8 \times \frac{\sqrt{2}}{2} = 4\sqrt{2}$$ 4. **Calculate the perimeter of the smaller square:** $$\text{Perimeter} = 4 \times \text{side length} = 4 \times 4\sqrt{2} = 16\sqrt{2}$$ 5. **Final answer:** The perimeter of the shaded square is $16\sqrt{2}$ units.