Two equivalent regular hexagonal-based prisms are divided and rearranged into 3 equilateral triangular-based prisms, as shown above. After rearrangement, the total surface area of all prisms has increased by 12.5% with the constant height.

If the height of each prism is \(\sqrt{3} \text{ cm}\), what is the side length of the regular hexagon base in \(\text{cm}\)?

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