To find the perimeter of the figure, we need to add up the lengths of all the outer sides. Let's identify and list each side using the labels provided:

1. Top side: $a - 3b$
2. Right vertical side (upper): $c$
3. Right horizontal side (middle): $3b$
4. Right vertical side (lower): $b + c$
5. Bottom side: $a - c$
6. Left vertical side (lower): $c$
7. Left horizontal side (middle): $2b + 2c$

Now, let's add all these side lengths to get the perimeter: $\text{Perimeter} = (a - 3b) + c + 3b + (b + c) + (a - c) + c + (2b + 2c)$

Next, we'll combine like terms:

• Terms with $a$: $a + a = 2a$
• Terms with $b$: $-3b + 3b + b + 2b = 3b$
• Terms with $c$: $c + c - c + c + 2c = 3c$

So, the simplified expression for the perimeter is: $2a + 3b + 3c$

Would you like more details, or do you have any questions about this solution?

Here are five related questions to consider:

1. What would be the perimeter if $a = 10$, $b = 5$, and $c = 2$?
2. How would the perimeter change if one of the side lengths was doubled?
3. Can you derive a formula for the area of this figure?
4. How would you express the perimeter if the figure was a regular polygon?
5. What happens to the perimeter if all variables $a$, $b$, and $c$ are equal?

Tip: Always double-check the figure to ensure you have included all the sides in your perimeter calculation.