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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.

Find the perimeter of the L-shaped figure with dimensions provided in inches. All angles are right angles.

Learn how to calculate the perimeter of an L-shaped figure with right angles using simple addition. This geometry problem is suitable for students in Grades 6-8 and involves the sum of the side lengths to find the perimeter.

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