How many 2 x 4 16 IOC studs needed for a room that is 224 sf?

depends on your spacing, 16" on center or 24" check your local building codes...and what your deck application is..Are you using a composite decking or wood..Couple of variables play into this...

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I'll Play:

Assuming 16" on center...

If you are using 8 foot 2x6's you will need 19.

If you are using 12 foot 2x6's over lapping 1 foot to make the 23" and supported along the center of the room you will need 14.

For 12" on center: 24(8ft) or 18(12ft)

For 24" on center: 13(8ft) or 10(12ft)

Note: depending on design/support, 2X6 may not be big enough for code (or safety).