If the length is cut into two parts a and b then a+b=l.
Let a be the part forming the square, then the side of the square is length a/4 and the radius of the circle is a/8.
The circumference of the circle has length b=2π(a/8)=πa/4. a/b=4/π, l=a+πa/4, therefore a=l/(1+π/4)=4l/(π+4).
The area of the circle=πa2/64 and the area of the square=a2/16.
The total area of the two figures is a2(π+4)/64.
In terms of l this is: (16l2/(π+4)2)((π+4)/64)=l2/(4π+16).