The problem asks to find the area of the shaded region, which involves a rectangle with a right triangle removed from it.

Step-by-Step Solution:

1. Area of the Rectangle: The rectangle has a length of 9 cm and a width of 6 cm. The area $A_{\text{rectangle}}$ is calculated as: $A_{\text{rectangle}} = \text{length} \times \text{width} = 9 \, \text{cm} \times 6 \, \text{cm} = 54 \, \text{cm}^2$

2. Area of the Right Triangle: The triangle has a base of 5 cm and a height of 2 cm. The area $A_{\text{triangle}}$ is: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \, \text{cm} \times 2 \, \text{cm} = 5 \, \text{cm}^2$

3. Shaded Area: To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle: $A_{\text{shaded}} = A_{\text{rectangle}} - A_{\text{triangle}} = 54 \, \text{cm}^2 - 5 \, \text{cm}^2 = 49 \, \text{cm}^2$

Thus, the area of the shaded region is 49 cm².

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

Here are 5 related questions to expand on this concept:

1. How do you find the area of composite shapes in general?
2. What is the formula for the area of a triangle and why is it different from a rectangle?
3. How would the calculation change if the triangle had been an equilateral triangle?
4. What would the perimeter of the shaded region be?
5. How can we use these concepts to calculate areas of irregular shapes?

Tip: Always break down complex shapes into simple ones (like triangles or rectangles) to calculate the area step by step.