@rlopez 

Good Morning Mr. Lopez,
   I hope your Thanksgiving Holiday was great.
   I looked at your solution. I should have recognized immediately that multiplying by "r" and substituting x^2 + y^2 for r^2 and also x=rcos(theta) and y=rsin(theta) would have provided me with the answer.
   I re-wrote the problem on paper and converted it to x and y and I did get to r^2 = 13/4. I also reviewed the plot below by by Kitonum 7570 and looked at his answers for area and length.
   I am still trying to figure out how my answers were double what you and Kitonum 7570 came up with. Also, I came to the same solution, r^2 = 13/4. Now I'm doubting what I was given credit for is actually correct.
   This is what I like about math, now I have something to dig around in and when I figure it out it will be the AHA moment that will solidify the learning. I'll talk with my TA next week. I'm wondering if the range of 0<=theta<=2Pi is the reason. I've re-ran the calculations on my calculator in various modes; function, polar, parameter, and I still get 22.65 for perimeter and 20.42^2 units for area.

No Response is necessary.
Thanks again,
Jay Crook.

@Carl Love 

Good Evening Mr. Love,
   Thank you for the followup and noticing that I had omitted squaring the second term. When I re-evaluated the area inside the curve, squaring the second term, it generated a value that was deemed correct on the quiz I've since recieved back from my TA.

Thank you for your quick response to my inquiry.

Jay Crook.

This is a follow up to my original post.

int(sqrt(((3*cos(theta)-2*sin(theta))^2)+(-3*sin(theta)-2*cos(theta))),theta=0..2*Pi);

I entered the above into Maple 2016 and it was evaluating for way too long, I think. This is the calculus formula for finding the length of a curve. I was able to get a value from my TI-84 Plus from the "fnInt(" function.

int(1/2*(3*cos(theta)-2*sin(theta))^2,theta=0..2*Pi);

The above is the calculus formula for the area inside/under/over the curve between 0..2Pi. This evaluated to 13Pi/2 in less than 5 seconds. This is what I got with my TI-84 Plus, but I'm not sure it's correct.

Thanks,
Jay.