Let one piece be of length x inches, which is formed into a square and let the other piece of length 34-x inches formed  into a circle.

 

The side length of square will be x/4 and its area will be  x2/16.

 

The circumference of the circle will be 34-x inches and if its radius is r,  then 2πr = 34-x.  This would give r = (34-x)/2π.  Area of circle = π{(34-x)2 /4π2}  = (34-x)2 / 4π

 

Total Area, A = x2 /16 + (34-x)2 / 4π