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For what you described, the roof and screened area seems quite small (6' X 10'). If you have the space, it may be that enlarging the square footage area you desire would be more cost effective and you'd get more "bang for your buck".
If you currently have a 6 X 10 concrete patio, it is more than likely that the slab thickness is not substantial enough to support the load of a roof and some foundation modifications may be required.
To meet current building codes will probably require that the slab be cut and reinforced footings be installed to carry the load.
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