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