The side of a square a = 2cm ( a = r ). Find the areas of: X, Y and Z.

Using some calculus  (and symmetry), we have  

 z = (in sq cm)             

I'll use a more exact value = 0.1735540900379272 sq cm.

And solving some equations, we have

4 - pi = y + 2z   →   y = 4 - pi - 2z  = 4 - pi - 2(0.1735540900379272) ≈ 0.5112991663343523615  sq cm

And

x + 3y + 2z = pi  →     x = pi - 3y - 2z =  

pi - 3(0.5112991663343523615) - 2( 0.1735540900379272)

≈  1.2605869745108817539626  sq cm

Check

x + 4y + 4z = 4  ???

1.2605869745108817539626+ 4(0.5112991663343523615 )+ 4(0.1735540900379272) =

3.9999999999999999999626  sq cm

Close enough  !!!!