https://file.aiquickdraw.com/mathbot/file/1730249249407ahn9e8ss.jpg

To solve for the missing side length, let's analyze the given dimensions and the structure of the figure.

1. **Understand the Shape**: This figure is made up of two rectangles joined together, with all intersecting sides meeting at right angles. To find the missing side length (labeled "?"), we’ll calculate based on the vertical alignment.

2. **Vertical Alignment**:
   - The total height of the figure (from top to bottom) can be calculated in parts:
     - The left side shows two vertical segments: one with length \(10 \, \text{ft}\) (top) and one with length \(6 \, \text{ft}\) (bottom).
   - Adding these segments together:
     \[
     10 \, \text{ft} + 6 \, \text{ft} = 16 \, \text{ft}
     \]
   - Therefore, the total height of the figure is \(16 \, \text{ft}\), which aligns with the right side.

3. **Finding the Missing Length**:
   - Since the total height on the left and right must match, and we know the height from the bottom is \(5 \, \text{ft}\), the missing segment at the top (marked with "?") must make up the rest of the \(16 \, \text{ft}\) height.
   - Set up the equation:
     \[
     ? + 5 \, \text{ft} = 16 \, \text{ft}
     \]
   - Solving for "?":
     \[
     ? = 16 \, \text{ft} - 5 \, \text{ft} = 11 \, \text{ft}
     \]

Thus, the missing side length is \( \boxed{11 \, \text{ft}} \).

Would you like a deeper explanation or have further questions?

Here are five related questions to expand on this problem:
1. How would you find the perimeter of this figure using the side lengths?
2. If the width of each segment doubled, how would that affect the perimeter?
3. How would you calculate the area of this figure?
4. What if the height of the top segment was unknown; how would that affect solving this problem?
5. How could we apply similar methods to solve for missing side lengths in three-dimensional figures?

**Tip:** When working with composite shapes, break them down into simpler parts to analyze their dimensions more easily.

Find the missing side length in a composite shape where intersecting sides meet at right angles. The given dimensions are 10 ft, 5 ft, 6 ft, 9 ft, and 16 ft.

This guide walks through finding a missing side length in a composite shape with right angles. Given dimensions include 10 ft, 5 ft, 6 ft, 9 ft, and 16 ft. Step-by-step solution for calculating the unknown side in this geometry problem, ideal for students in Grades 5-7.

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