From the image, I can see a pattern of regular hexagons inscribed in a square of side length 10 units. You are asking for the side lengths of the equilateral hexagons (marked with question marks).

To find the side length of the hexagon:

1. Consider the relationship between the side length of a regular hexagon and its inscribed circle. The hexagon fits perfectly into the square grid, and since the square has a side length of 10 units, we can use the geometry of the hexagon.

2. The distance across two opposite vertices of a regular hexagon is twice the side length, which is equivalent to the diameter of the circle inscribing the hexagon.

3. The hexagons fit into the square in such a way that the overall width of the hexagons fills the 10-unit side of the square.

Let me compute this step-by-step to find the side length of the hexagons.

I'll start with the assumption that three hexagons aligned side by side across the diagonal or the edge of the square should give us the key geometric relationships. Let me calculate the precise length.The side length of each equilateral hexagon is approximately 2.89 units.

Would you like more details about how this was calculated or have further questions?

Here are five related questions to expand on this:

1. How do you calculate the area of a regular hexagon given its side length?
2. What is the relationship between the side length and the radius of a circle inscribing a regular hexagon?
3. How would the arrangement change if the square had a different side length?
4. How can the perimeter of each hexagon be calculated from the side length?
5. How can you fit the maximum number of hexagons into a larger square?

Tip: For regular polygons, the key geometric properties often involve symmetry and simple ratios between side lengths and diagonals!