https://file.aiquickdraw.com/mathbot/file/17262983271469cfuirlm.jpg

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.

Find the perimeter of the shaded part (use π = 3.14). The figure is a square with one side being 8 units and the shaded region is a quarter circle.

This problem involves finding the perimeter of a shaded quarter-circle inside a square with side lengths of 8 units. Learn how to apply the circumference formula for circles and calculate composite figures' perimeters. Suitable for students in Grade 6-8.

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