https://file.aiquickdraw.com/mathbot/file/1728759168422qpctgvvf.jpg

To solve for the missing length in this L-shaped figure, let's first outline the given dimensions:

- Vertical sides: 4 cm, 6 cm, and 10 cm
- Horizontal sides: One unknown (let's call it \( x \)), and two known lengths: 10 cm and 6 cm.

### Step-by-Step Solution:
1. **Perimeter Formula**:
   The perimeter of the shape is the total length around the edges. So we can express the perimeter as the sum of all the sides:
   \[
   P = 4 + 6 + 10 + 6 + 10 + x
   \]
2. **Known Total Perimeter**:
   We know from the problem that the total perimeter is 38 cm.
   \[
   4 + 6 + 10 + 6 + 10 + x = 38
   \]
3. **Simplify the Equation**:
   First, sum up the known lengths:
   \[
   36 + x = 38
   \]
4. **Solve for \( x \)**:
   Subtract 36 from both sides:
   \[
   x = 2
   \]

So, the missing length in the box should be **2 cm**.

Would you like further details on this solution or explanations on perimeter calculation?

### Related Questions:
1. How do you calculate the perimeter of an irregular polygon?
2. If the shape had different side lengths, how would the perimeter change?
3. What is the difference between perimeter and area?
4. Can you explain how different side measurements affect the overall shape?
5. How do you calculate the area of this L-shaped figure?

### Tip:
Always double-check that all sides of a shape are included when calculating the perimeter to avoid missing any length!

The perimeter of this shape is 38 cm. What number should go in the box?

Learn how to solve a geometry problem involving the perimeter of an L-shaped figure with a missing side length. Using perimeter calculations, this step-by-step solution helps you find the unknown side. Suitable for students in Grades 4-6.

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