What do you think guys is it possible to do it ?
If you simply want to make a distance meter with a built-in calculator, I'm sure it is possible.
The $500 budget suggests you are planning is a rotating device that scans the room looking for corners by the change in readings. This would check for square calculating hypoteneuses and build up the room by triangulation.
If that is the plan, probably not, or at least not in a practical manner.
The first thing to find out is does such a device already exist? If not, why not?.
The first place to check is probably Leica Disto. If anybody makes one, it is probably them and I don't think they do. So that is the if.
As for the why, while there are plenty of distance measuring devices, using them in a device to calculate area would probably multiply their shortcomings by thousands. One thing you can be sure about is that lack of demand is not among the whys. If you can pull this off, you probably on your way to making your fortune.
Trust me, I'm a professional. If I want the area of a room, I get the relevant distances and calculate the area on a calculator. If the room is very complicated, I get the relevant distances, draw the room in CAD and let it calculate the area. The latter is a one-button operation. In both cases the actual area calculation could never be more than 5% of the time taken to do the job.
The above is a comment on what is practical, not what is possible, but there is a vital ingredient in there. That is the word relevant. The process takes in human intervention to determine what is relevant an what is not, and the latter exceeds the former.
The biggest problem the Arduino has is probably in determining what is relevant. Even if the room is left bare, that is still the biggest problem. To be of any use the ranging has to be accurate, That might not be very hard but, the more accurate the ranging is, the bigger the problem of relevance becomes. It isn't hard to imagine a team of workers rolling up their tapes and going home to dinner while your Arduino is still there trying to work out if a corner is actually a door jamb.