Alright, you'll have to excuse me if I get this question wrong. Not feeling very well today. 
The distance around the pool would be the circumference.
Considering the pool is a circle.
The formula to get the circumference of a circle is 2*pi*r.
So, we have the equation 2*pi*r = 38.
Divide both sides by 2 to get pi*r = 19.
Divide both sides by pi to get r = 19/pi. Put that in a calculator and get r = 6.0478878374920228...
Don't round it yet. Well, you could, but you would get a less accurate answer.
The formula to get the area of a circle is pi*r^2.
So we plug in r (which is 6.0478878374920228) into this equation.
pi*(6.0478878374920228)^2
Just plug that all into a calculator and get 114.9098689123484339749.
Round that to the nearest hundredth and get 114.91 feet^2 (Because it's the area)
114.91 feet^2.
