I have decided to enclose the carport so I can have a small home gym. The carport is adjacent to a smaller house on the property, so it seemed most sensible to lay a wooden floor structure in that part as well if you want to increase the area inside that house in the future. See drawing.

The new part will be used as a gym/office. And after some searching here on the forum, I saw that there is something called EPS concrete? Is it suitable to use in this case?

If yes, could you roll out a gym mat directly on the EPS concrete?

And lastly, will this solution be more expensive than pouring a slab? I have received a quote of 36' for a 120mm slab with 100mm insulation.

What I want is a strong durable floor suitable for a gym.
 
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Blueprint showing a layout with a carport, storage rooms, a hobby room of 27.5 sqm, and a fireplace. Dimensions and labels included.
Here is the drawing
 
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