To find the perimeter of the given figure, let’s carefully analyze the lengths of all sides.

Step 1: Observing the shape

The shape appears to be a step-like figure made up of multiple horizontal and vertical segments. The dimensions provided are:

• Horizontal segments: 10 cm and 8 cm.
• Vertical segments: 12 cm.

Step 2: Break down the segments

Let’s identify the perimeter by summing all the outer edges. From the structure:

1. Top horizontal edge: 10 cm.
2. Right vertical edge: 12 cm.
3. Bottom horizontal edge: 8 cm.
4. Left vertical edge: (This is split into two parts: $12 - 8 = 4$ cm for the inner left segment, and an additional 8 cm for the bottommost vertical segment).

The full left vertical side is: $4 + 8 = 12$ cm.

Step 3: Perimeter calculation

The perimeter $P$ is the sum of all the outer edges: $P = \text{Top edge} + \text{Right edge} + \text{Bottom edge} + \text{Left edge}$ Substituting values: $P = 10 + 12 + 8 + 12 = 42 \, \text{cm}.$

Final Answer:

The perimeter of the figure is 42 cm.

Would you like more details or clarification?

Here are 5 related questions to consider:

1. How do you calculate the perimeter of irregular shapes in general?
2. What is the difference between perimeter and area?
3. How can this concept be extended to 3D objects (like finding surface area)?
4. How do you ensure all segments are accounted for in similar problems?
5. What units are appropriate when calculating perimeters?

Tip: When solving for the perimeter of irregular shapes, carefully verify that all outer edges are included, and avoid double-counting any internal segments!