To find the area of the shaded region, we need to calculate the area of the rectangle and subtract the area of the circle from it.

Step-by-Step Solution:

1. Find the Area of the Rectangle:

   • The rectangle has dimensions of $11 \, \text{cm} \times 11 \, \text{cm}$.
   • Area of the rectangle $= 11 \times 11 = 121 \, \text{cm}^2$.

2. Find the Area of the Circle:

   • The circle has a radius of $5 \, \text{cm}$.
   • Area of the circle $= \pi \times r^2 = \pi \times 5^2 = 25\pi \approx 78.54 \, \text{cm}^2$.

3. Calculate the Area of the Shaded Region:

   • The shaded region is the area of the rectangle minus the area of the circle.
   • Shaded area $= 121 - 78.54 \approx 42.46 \, \text{cm}^2$.

Final Answer:

The area of the shaded region is approximately 42.46 cm².

Would you like further details on any part of this calculation?

Here are some related questions for further exploration:

1. How would the shaded area change if the circle's radius were increased to 6 cm?
2. What would the shaded area be if the rectangle dimensions were doubled?
3. How can you calculate the area if the circle were only partially inside the rectangle?
4. What is the formula for the area of a circle in terms of its diameter instead of radius?
5. How would the solution change if the rectangle were a different shape, like a square or parallelogram?

Tip: For problems involving areas, always remember to match units and double-check that all dimensions are correctly applied in your formulas.