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Find the perimeter of the following illustrations. Note: the same marks indicate the same illustrations 

To find the perimeter of the given shape, we'll sum the lengths of all its sides. 

### Analyzing the Shape:
- The shape is a polygon with a step-like pattern.
- The marks on the sides indicate equal lengths.
- The marked sides on the right edge are 3 cm each.

### Steps:
1. **Identify the lengths of all sides**:
    - The marked sides indicate equal lengths.
    - The vertical and horizontal segments can be identified by their alignment with the marked 3 cm side.

2. **Calculate the perimeter**:
    - There are multiple horizontal and vertical segments of varying lengths.

Since the vertical edge is 3 cm (the same length as the marked segments), and since each step is composed of a combination of marked and unmarked segments, we need to count both horizontal and vertical lengths.

Let's consider each segment:
- The horizontal sides total (from left to right): \(3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} = 9 \, \text{cm}\).
- The vertical sides (top to bottom): \(3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} = 9 \, \text{cm}\).

However, we need to sum each small segment separately:

- For **Horizontal Segments**: \(3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm}\) = \(12 \, \text{cm}\).
- For **Vertical Segments**: \(3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm}\) = \(12 \, \text{cm}\).

### **Perimeter Calculation**:
The total perimeter \( P \) = \(12 \, \text{cm} \) (horizontal) + \(12 \, \text{cm} \) (vertical) = \(24 \, \text{cm} \).

### Final Answer:
The perimeter of the shape is **24 cm**.

Would you like more details on how the lengths were identified or the reasoning behind the calculations?

### Related Questions:
1. How do you calculate the area of this shape?
2. What is the perimeter of a shape if only one side length is known?
3. How would the perimeter change if the shape was scaled by a factor of 2?
4. How can you verify the perimeter calculation by measuring the actual sides?
5. How does understanding perimeter help in real-life applications, like fencing a garden?

**Tip:** When solving perimeter problems, always ensure all sides are accounted for, especially when dealing with complex shapes.

Discover how to find the perimeter of a polygon with equal side lengths using a step-by-step guide. This problem involves calculating the total length of all sides of a polygon with marked equal segments. Suitable for students in Grades 4-6.

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