https://file.aiquickdraw.com/mathbot/file/1726358716856s5r4k2cq.jpg

Let's work through this perimeter problem by analyzing the shape and the measurements provided in the image.

### Shape Overview:
- The figure has a combination of vertical and horizontal segments, forming a step-like shape. 
- All interior angles are right angles, meaning we are dealing with an L-shaped figure made of rectangles.
  
### Dimensions:
- From the top to bottom:
  - The height of the entire shape is \( 12 \, \text{cm} \).
  - The shorter internal vertical side measures \( 4 \, \text{cm} \).
- From left to right:
  - The full length at the top of the shape is \( 10 \, \text{cm} \).
  - The shorter internal horizontal side measures \( 6 \, \text{cm} \).

### Steps to Find the Perimeter:
The perimeter is the total length around the shape. You need to sum all outer edges:

1. Top side: \( 10 \, \text{cm} \)
2. Right vertical side: \( 10 \, \text{cm} \)
3. Bottom horizontal side: \( 6 \, \text{cm} \)
4. Bottom left vertical side: \( 12 \, \text{cm} \)
5. Small middle horizontal side (inner): \( 4 \, \text{cm} \)
6. Left vertical side (inner): \( 6 \, \text{cm} \)

Now, adding all these sides:

\[
P = 10 + 10 + 6 + 12 + 4 + 6 = 48 \, \text{cm}
\]

### Final Answer:
The perimeter of the shape is \( \mathbf{48 \, \text{cm}} \).

Would you like more details on any part of this solution?

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Here are 5 related questions you can explore:
1. How do you calculate the area of this irregular shape?
2. How would the perimeter change if one of the side lengths were doubled?
3. What is the difference between perimeter and area in geometry?
4. How do you handle perimeter calculations for shapes with curves?
5. How can you find the perimeter of more complex 3D shapes?

**Tip:** When solving perimeter problems, ensure to account for all outer sides and avoid including internal segments.

Work out the perimeter of the following shape.

Learn how to calculate the perimeter of an L-shaped figure with right angles. This problem covers key geometric concepts, including perimeter calculations and right-angle properties. Suitable for students in Grades 6-8.

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