To solve this problem, we need to find the perimeter of the shaded region, which consists of two parts:

1. The curved part, which is a quarter of a circle.
2. The straight part along the square.

Step-by-step solution:

1. Straight part of the perimeter:

   • The length of each side of the square is given as 8 units.
   • The shaded region includes one full side of the square. Therefore, one straight part of the perimeter is 8 units.

2. Curved part of the perimeter (quarter of a circle):

   • The radius of the circle is also 8 units (same as the side of the square).
   • The circumference of a full circle is given by $2\pi r$, where $r = 8$.
   • So, the circumference of the full circle is $2 \times 3.14 \times 8 = 50.24$ units.
   • Since the shaded region contains a quarter of the circle, the curved part is $\frac{1}{4} \times 50.24 = 12.56$ units.

3. Total perimeter:

   • The total perimeter of the shaded region is the sum of the straight part and the curved part: $\text{Total perimeter} = 8 + 12.56 = 20.56 \, \text{units}$

It seems like the correct option should be very close to $20.56$, but the provided answer options don't include this exact value. This may be a slight error or rounding issue in the problem's answer choices.

Would you like to explore further details, or do you have any questions?

Here are five related questions:

1. How do you calculate the circumference of a circle?
2. What is the formula for the perimeter of any shape?
3. What is the relationship between the radius and circumference of a circle?
4. How can you find the perimeter of other quarter-circle figures?
5. What role does $\pi$ play in circular geometry?

Tip: Always double-check calculations involving $\pi$, especially when approximations like $\pi = 3.14$ are used.