Appropriate usage
Solution 1:
"Take this seat" would be fine if you want the other person to sit in a specific seat; you might want to add a "please". If the choice of seat doesn't matter, or there is only one seat available, "take a seat" sounds more natural to me. Also, "take a seat" is a gesture to someone to have/take a seat so as to not keep him/her standing or it is considered an act of kindness.
Credit: nnnnnn