This compound shape can be divided into two rectangles. Let’s calculate the area step by step.

Step 1: Divide the Shape

We can split the L-shaped figure into two rectangles:

1. Rectangle A (the vertical section on the left).
2. Rectangle B (the horizontal section on the bottom right).

Step 2: Calculate the Dimensions

• Rectangle A: The height is $7 \, \text{cm}$ and the width is $3 \, \text{cm}$.
• Rectangle B: The width is $8 \, \text{cm}$ and the height is $3 \, \text{cm}$.

Step 3: Calculate Areas

• Area of Rectangle A:
  $\text{Area} = \text{height} \times \text{width} = 7 \times 3 = 21 \, \text{cm}^2$

• Area of Rectangle B:
  $\text{Area} = \text{height} \times \text{width} = 3 \times 8 = 24 \, \text{cm}^2$

Step 4: Add the Two Areas

Total area of the compound shape:
$\text{Total Area} = 21 + 24 = 45 \, \text{cm}^2$

Final Answer:

The area of the compound shape is 45 cm².

Do you want me to explain any step further?

Here are 5 related questions to deepen understanding:

1. How would you calculate the area if the two sections were overlapping instead of separate?
2. What if the dimensions of one rectangle were unknown—how would you approach solving for it?
3. How does the perimeter of this shape differ from its area calculation?
4. Can you determine the area if the shape had irregular curves added to one side?
5. How would scaling this shape (doubling all dimensions) affect its area?

Tip: When dividing a compound shape, always ensure no part of the figure is missed or double-counted!