To find the perimeter of this L-shaped figure, we need to sum the lengths of all its outer sides.

The outer sides are labeled as:

• One side: $6v + 1$
• One vertical side: $4$
• Another vertical side: $5v$
• The short horizontal side at the bottom: $3$

Looking at the figure, we can deduce the other two lengths needed. Since the shape is L-shaped:

• The horizontal length at the top is $6v + 1$, and the total horizontal length of the entire shape (including the short side at the bottom) would be the same. Thus, the horizontal length of the bottom side is already $3$, so the missing horizontal part is $6v + 1 - 3 = 6v - 2$.

• Similarly, the total vertical height is made up of the two vertical sides: $5v$ and $4$, so no new length needs to be added vertically.

Now, sum all these lengths to calculate the perimeter:

$\text{Perimeter} = (6v + 1) + 4 + 5v + 3 + (6v - 2)$

Simplify this expression:

$\text{Perimeter} = 6v + 1 + 4 + 5v + 3 + 6v - 2$

Combine like terms:

$\text{Perimeter} = (6v + 5v + 6v) + (1 + 4 + 3 - 2)$

$\text{Perimeter} = 17v + 6$

Thus, the perimeter of the shape is:

$\boxed{17v + 6}$

Would you like further explanation on any of the steps, or do you have any questions?

Here are some related questions to consider:

1. How do you calculate the perimeter of irregular shapes?
2. What would the expression be if the shorter horizontal side was different?
3. How does adding or removing parts of the shape affect the perimeter?
4. Can you apply this process to find the area of the same shape?
5. How would the expression for the perimeter change if the dimensions were doubled?

Tip: Always visualize the shape in terms of smaller, simpler components to easily calculate perimeters and areas.