To solve this problem, we need to calculate the perimeter of the figure shown in the diagram. Here's the approach:

Key Details:

• All angles are right angles.
• AB = 4 and BC = 5.
• The figure consists of a series of steps, all of which are aligned vertically and horizontally.

Step-by-Step Solution:

1. Analyze the Shape:

   • The figure is composed of a series of vertical and horizontal line segments. The total length of these line segments adds up to the perimeter.

2. Horizontal Segments:

   • The horizontal base, $BC = 5$, and other horizontal segments correspond to smaller steps.
   • Since all vertical segments add up to $AB = 4$, the horizontal segments must also sum to $BC = 5$.

3. Vertical Segments:

   • The vertical side $AB = 4$ and additional vertical segments correspond to the "steps" of the figure.

4. Calculate Total Perimeter:

   • Total perimeter = Sum of all vertical segments + Sum of all horizontal segments.
   • For this type of stepped figure, the total vertical length is the same as $AB + BC = 4 + 5$, and the total horizontal length is also $AB + BC = 4 + 5$.
   • Therefore, the total perimeter = $2 \times (AB + BC) = 2 \times (4 + 5) = 18$.

Final Answer:

The perimeter of the entire figure is 18.

Answer: (C) 18

Do you want further clarification or details? Here are five related questions to expand your understanding:

1. How would the solution change if one of the side lengths were different?
2. Can you explain why the total vertical and horizontal lengths are equal in such shapes?
3. How does the stepped design affect the calculation of perimeter versus area?
4. What other methods could you use to verify the perimeter calculation?
5. How do right angles simplify geometric problems like this?

Tip: Always break a complex figure into simpler parts for easier calculations!