To find the area of the given shape, we can break the problem into simpler parts.

Step 1: Find the area of the outer rectangle.

The outer rectangle has a width of 8 cm and a height of 7 cm.

$\text{Area of outer rectangle} = 8 \, \text{cm} \times 7 \, \text{cm} = 56 \, \text{cm}^2$

Step 2: Find the area of the cut-out part.

The cut-out section is a smaller rectangle with dimensions of width $3 \, \text{cm}$ and height $(1 + 3 + 2) \, \text{cm} = 6 \, \text{cm}$.

$\text{Area of cut-out} = 3 \, \text{cm} \times 6 \, \text{cm} = 18 \, \text{cm}^2$

Step 3: Subtract the cut-out area from the outer rectangle area.

$\text{Total area} = 56 \, \text{cm}^2 - 18 \, \text{cm}^2 = 38 \, \text{cm}^2$

Therefore, the area of the given shape is $38 \, \text{cm}^2$.

Would you like a detailed breakdown of any part of this solution or have any other questions?

Related Questions

1. How would you calculate the perimeter of this shape?
2. If the dimensions of the outer rectangle were doubled, what would be the new area?
3. What would be the area of the shape if only half of the cut-out section was removed?
4. How can you determine the area of shapes with multiple cut-outs?
5. What is the difference between finding the area of a compound shape versus a simple shape?

Tip

Always break down complex shapes into smaller, familiar shapes (e.g., rectangles, triangles) to simplify calculations.