In the given hexagon, the numbers within each segment seem to follow a pattern involving the numbers around the perimeter. Here's how the pattern can be analyzed:

1. The central number is 1.
2. The numbers within the hexagon's segments (100, 64, 36, 121, 144) are perfect squares:
   • $100 = 10^2$
   • $64 = 8^2$
   • $36 = 6^2$
   • $121 = 11^2$
   • $144 = 12^2$

The numbers surrounding the hexagon represent a specific relationship with these squares:

• Side 4 corresponds to 100 (i.e., 10), which may hint at a relationship between the number and the side.
• Side 3 corresponds to 64 (i.e., 8).
• Side 2 corresponds to 36 (i.e., 6).
• Side 6 corresponds to 121 (i.e., 11).
• Side 5 corresponds to 144 (i.e., 12).

Missing Number Analysis:

Looking at the side marked as 4 and the missing number:

• The side is 4, and the corresponding perfect square should be related to this value. Given the other patterns, it could be the square of 7.

Thus, the missing number should be: $7^2 = 49$

The missing number is 49.

Would you like further clarification or details?

Here are 5 related questions:

1. How do perfect squares relate to real-world geometric patterns?
2. Can we generalize this pattern for polygons with more sides?
3. How can we deduce patterns when numbers seem random?
4. What are the properties of perfect squares, and how are they used in puzzles?
5. How does the arrangement of shapes affect mathematical patterns?

Tip: Always check for numerical patterns like squares, cubes, or arithmetic sequences when solving puzzles with missing numbers.