From the image, the problem is about finding the area of a shaded region formed by removing a right triangle from a rectangle.

Step-by-step Solution:

1. Area of the Rectangle:

   • The dimensions of the rectangle are 9 cm (base) and 6 cm (height).
   • The formula for the area of a rectangle is: $\text{Area of Rectangle} = \text{Base} \times \text{Height}$ Substituting the values: $\text{Area of Rectangle} = 9 \times 6 = 54 \, \text{cm}^2$

2. Area of the Right Triangle:

   • The dimensions of the triangle are 6 cm (base) and 2 cm (height).
   • The formula for the area of a right triangle is: $\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$ Substituting the values: $\text{Area of Triangle} = \frac{1}{2} \times 6 \times 2 = 6 \, \text{cm}^2$

3. Area of the Shaded Region:

   • The shaded region is obtained by subtracting the area of the triangle from the area of the rectangle: $\text{Area of Shaded Region} = \text{Area of Rectangle} - \text{Area of Triangle}$ Substituting the calculated values: $\text{Area of Shaded Region} = 54 - 6 = 48 \, \text{cm}^2$

Final Answer:

The area of the shaded region is 48 cm².

Would you like further explanation on any step?

Follow-up Questions:

1. How do you derive the area formulas for rectangles and triangles?
2. Can this approach be used for more complex shapes involving circles or polygons?
3. What are some real-world applications of finding areas of shaded regions?
4. How do we ensure correct units in calculations involving areas?
5. How would the solution change if the triangle had different dimensions?

Tip: Always double-check your calculations, especially when dealing with subtraction of areas, to ensure accuracy.