We need to calculate the perimeter of the shaded shape, which is a rectangle with a semicircle removed from one of its longer sides. Here's how we can proceed:

Step-by-Step Breakdown:

1. Rectangle Perimeter (without semicircle): The full perimeter of the rectangle is given by the sum of the lengths of all four sides: $P_{\text{rectangle}} = 2 \times (\text{length} + \text{width}) = 2 \times (38 \, \text{cm} + 12 \, \text{cm}) = 2 \times 50 \, \text{cm} = 100 \, \text{cm}.$

   However, this includes the entire length of $BC$ (11 cm) which is partially cut by the semicircle, so we must subtract part of this.

2. Semicircle: The semicircle is cut out from the side $BC$. The diameter of the semicircle is equal to the width of the rectangle, which is 12 cm. The circumference $C$ of a full circle is given by: $C = \pi \times d,$ where $d$ is the diameter. For a semicircle, the perimeter of the curved part is half of this: $C_{\text{semicircle}} = \frac{1}{2} \times \pi \times 12 \, \text{cm} = 6\pi \, \text{cm}.$ Using $\pi \approx 3.1416$: $C_{\text{semicircle}} \approx 6 \times 3.1416 = 18.85 \, \text{cm}.$

3. Total Perimeter of the Shaded Shape: To get the perimeter of the shaded shape, we need to adjust the rectangle's perimeter by removing the straight line segment $BC$ (which is 12 cm) and adding the semicircular arc instead (18.85 cm). So, the total perimeter is: $P_{\text{shaded}} = 100 \, \text{cm} - 12 \, \text{cm} + 18.85 \, \text{cm} = 106.85 \, \text{cm}.$

Final Answer:

The perimeter of the shaded shape is approximately 106.85 cm to two decimal places.

Do you have any questions or would you like further details on any step?

Here are 5 related questions for further practice:

1. What is the area of the shaded shape?
2. How would the perimeter change if the diameter of the semicircle were increased to 14 cm?
3. What is the perimeter if a full circle is removed instead of a semicircle?
4. How do we calculate the perimeter of a quarter circle added to a rectangular shape?
5. How would you find the perimeter if the semicircle was cut out from a different side of the rectangle?

Tip: Remember to adjust the original shape's perimeter whenever a portion of it is replaced by a curved section, like a semicircle.