The problem asks for the area of the shaded region, where a circle with a radius of 1 cm is inside a rectangle with dimensions 11 cm by 12 cm.

Steps to solve:

1. Find the area of the rectangle: $\text{Area of rectangle} = \text{length} \times \text{width} = 11 \, \text{cm} \times 12 \, \text{cm} = 132 \, \text{cm}^2$

2. Find the area of the circle: The radius of the circle is 1 cm, so the area of the circle is given by: $\text{Area of circle} = \pi \times r^2 = \pi \times 1^2 = \pi \, \text{cm}^2$ Using $\pi \approx 3.1416$: $\text{Area of circle} \approx 3.1416 \, \text{cm}^2$

3. Find the area of the shaded region: The shaded region is the area of the rectangle minus the area of the circle: $\text{Shaded area} = \text{Area of rectangle} - \text{Area of circle} = 132 \, \text{cm}^2 - 3.1416 \, \text{cm}^2 \approx 128.86 \, \text{cm}^2$

So, the area of the shaded region is approximately 128.86 cm², rounded to the nearest hundredth.

Would you like further details or have any questions?

Here are five related questions you could explore:

1. What would happen to the shaded area if the circle's radius doubled?
2. How does the area change if the rectangle's dimensions increase by 50%?
3. What is the perimeter of the shaded region, excluding the circle's perimeter?
4. How would the shaded area change if the circle were placed in a square of the same area?
5. What would be the area of the shaded region if the circle's radius was 2 cm?

Tip: When solving problems involving both a circle and a rectangle, it’s often useful to start by calculating their individual areas separately and then combine or subtract them as needed.