Your first trester is 14 weeks. You are actually pregnant 10 months, not 9. 40 divided by 4 is 10.
And again, we are currently in the only month of the year that has only four weeks in it. On average, there are 4.3 weeks in a month. 40 weeks is 9 months and one week, not even close to 10 months. Check out a calendar - there are 52 weeks in a year but that doesn't make 13 months.
To the OP - the thirteenth week is part of the third month, and part of the first trimester. Once this week is over and you hit week 14, you will start the second trimester and your fourth month of pregnancy.