Let's focus on problem 10, where we are asked to find the perimeter of the L-shaped figure. The dimensions are given in inches, and all angles are right angles. Here's how we solve it:

Step-by-Step Process:

1. Identify the lengths of all sides:

   • The top horizontal segment is $25$ inches.
   • The right vertical segment is $51$ inches.
   • The two lower vertical segments are $9$ inches and $19$ inches.
   • The two horizontal segments below the top one are $23$ inches and $15$ inches.

2. Total perimeter calculation: The perimeter of a polygon is the sum of all its side lengths. For this L-shape, we need to sum the lengths of the outer edges.

   Perimeter = $25$ + $51$ + $9$ + $15$ + $23$ + $19$

3. Perform the arithmetic: $25 + 51 + 9 + 15 + 23 + 19 = 142 \, \text{inches}$

So, the perimeter is 142 inches.

Would you like further details or have any questions? Here are five related questions that can expand your understanding:

1. How would you calculate the area of this L-shaped figure?
2. Can you determine the perimeter of more complex polygons using this method?
3. How do you handle missing sides when calculating the perimeter?
4. Can we use a formula to directly calculate the perimeter of certain shapes, like circles or squares?
5. How does the perimeter relate to the area of a figure?

Tip: Always ensure that you count all sides when calculating the perimeter, especially with irregular shapes.