Let's solve the two problems step-by-step.

Problem 1:

We need to find the area of the given L-shaped compound figure.

Solution:

1. Break the shape into two rectangles:

   • Rectangle A (top part): Dimensions are $3 \, \text{cm} \times 3 \, \text{cm}$.
   • Rectangle B (bottom part): Dimensions are $8 \, \text{cm} \times 6 \, \text{cm}$ (height is $9 - 3 = 6 \, \text{cm}$).

2. Calculate the area of each rectangle:

   • Area of Rectangle A: $3 \times 3 = 9 \, \text{cm}^2$.
   • Area of Rectangle B: $8 \times 6 = 48 \, \text{cm}^2$.

3. Add the areas of the two rectangles:
   Total Area = $9 + 48 = 57 \, \text{cm}^2$.

Problem 2:

We need to calculate the area of the second L-shaped compound figure.

Solution:

1. Break the shape into two rectangles:

   • Rectangle A (top part): Dimensions are $10 \, \text{cm} \times 4 \, \text{cm}$.
   • Rectangle B (left part): Dimensions are $2 \, \text{cm} \times 9 \, \text{cm}$ (height is $13 - 4 = 9 \, \text{cm}$).

2. Calculate the area of each rectangle:

   • Area of Rectangle A: $10 \times 4 = 40 \, \text{cm}^2$.
   • Area of Rectangle B: $2 \times 9 = 18 \, \text{cm}^2$.

3. Add the areas of the two rectangles:
   Total Area = $40 + 18 = 58 \, \text{cm}^2$.

Final Answers:

1. Problem 1: $57 \, \text{cm}^2$
2. Problem 2: $58 \, \text{cm}^2$

Would you like additional details or clarifications?

Related Questions:

1. How can we calculate the perimeter of such compound shapes?
2. What happens if dimensions are given in meters instead of centimeters?
3. Can we calculate the area if one of the lengths or widths is unknown?
4. How would you approach these problems if the shapes were in three dimensions?
5. How does scaling (e.g., doubling dimensions) affect the area of the shape?

Tip:

Always label and break compound shapes into smaller, simpler components for easier calculations.