To calculate the perimeter of the irregular polygon in the image, we need to sum the lengths of all the outer sides.

From the image, we can see these dimensions:

• The top side: $15.8 \, \text{cm}$
• The right side: $14.7 \, \text{cm}$
• The left side: $7.2 \, \text{cm}$

The stepped part consists of three horizontal and vertical sections. To calculate their lengths, let's break it down:

• The middle horizontal section: appears to be equal to $15.8 \, \text{cm} - 7.2 \, \text{cm} = 8.6 \, \text{cm}$
• The middle vertical section is aligned with the top-left vertical, which is $14.7 \, \text{cm} - 7.2 \, \text{cm} = 7.5 \, \text{cm}$

Now, summing the sides:

$P = 15.8 \, \text{cm} + 14.7 \, \text{cm} + 7.2 \, \text{cm} + 8.6 \, \text{cm} + \text{other sections (to be calculated)}$

Let me calculate the missing vertical and horizontal components.The perimeter of the polygon is approximately $53.8 \, \text{cm}$.

Would you like further details on how the perimeter was calculated or have any other questions?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the perimeter of irregular shapes?
2. Can you break down the formula for finding the perimeter of a rectangle?
3. What is the difference between perimeter and area?
4. How would the perimeter change if one side of the shape was doubled?
5. Can you think of other practical examples where you need to calculate the perimeter?

Tip: Always make sure that all sides are included when calculating the perimeter of any shape.