https://file.aiquickdraw.com/mathbot/file/1726939079987vufhauan.jpg

The problem in the image is asking for the missing side length in a geometric figure, assuming all intersecting sides meet at right angles.

### Steps to Solve:

1. We are given:
   - A vertical length on the left of 9 cm.
   - Another vertical length on the right of 4 cm.
   - A horizontal length of 16 cm at the top.
   - A horizontal length of 10 cm at the bottom.
   - A middle horizontal segment measuring 6 cm.

2. The total vertical length of the figure (on the left) is made up of two vertical segments: 9 cm at the top and an unknown length (which we need to find) at the bottom.

3. Since all sides are at right angles and the horizontal segments must align, the missing side length can be found using subtraction:
   - The total length of the right side is the same as the total length of the left side.
   - Total vertical length on the right = \(9 \, \text{cm} + \text{unknown length}\)
   - The vertical length on the right is 4 cm.

   To find the missing length:
   \[
   \text{Missing length} = 9 \, \text{cm} - 4 \, \text{cm} = 5 \, \text{cm}
   \]

Thus, the missing side length is **5 cm**.

Would you like more details on how this was solved or any clarification?

### Follow-up Questions:
1. How do you calculate the total perimeter of this shape?
2. What method would you use to calculate the area of this irregular shape?
3. What are the properties of a rectangle that were helpful in solving this problem?
4. Can you solve for the area of this figure by dividing it into smaller rectangles?
5. How would the approach change if the angles were not right angles?

### Tip:
When solving problems involving unknown side lengths, using the properties of right angles and symmetry in geometry can simplify the process considerably.

Find the missing side length. Assume that all intersecting sides meet at right angles. The given lengths are: 9 cm, 4 cm, 16 cm, 6 cm, and 10 cm.

Learn how to find the missing side length in a geometric figure assuming all intersecting sides meet at right angles. This problem covers key geometric concepts and simple subtraction, suitable for students in Grades 6-8.

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