Hello all!

I need some help. This is my first time using Mathematica for an assignment, and my teacher and I are stumped. I have put in two equations that define a third. When I try to put in a number for x, Mathematica won't give me a simplified answer. I have tried the Simplify, FullSimplify, N, ?NumericQ, and a few other commands I can't think of. It just keeps giving me this expression with pi and some decimals but never an actually numeric answer, which is what I need. What am I doing wrong?

R[x_] := 2 + Sqrt[1-x^2]

r[x_] := 2 - Sqrt[1 - x^2]

A[x_?NumericQ] := [Pi][R[x]]^2 - [Pi][r[x]]^2

(1/2)A[1/2]

1/2 (-\[Pi][2 - Sqrt[3]/2]^2 + \[Pi][1/2 (4 + Sqrt[3])]^2)

The last part is what I keep getting. Sometimes I can get it to give me decimals instead of pi and the radicals, but it won't actually solve the equation. Can anyone tell me why?

Thanks!