Question 1208131
Take what the other post said.  The original length is 10.
Cut to make both pieces into one square and one circle.
The question is to use x as the side of the square shape.  This mean that its perimeter
must be 4x.


So what are the two cut lengths you start with?
4x for the square and 10-4x for the circumference of circle.


Area of square, {{{x^2}}}.


Area if circle, {{{pi*r^2}}}
Circumference, {{{10-4x=2pi*r}}}
which means {{{r=(10-4x)/(2pi)}}}.


The circle's area then must be {{{pi((10-4x)/(2pi))^2}}}
or, {{{((10-4)^2)/(4pi)}}}.


The TOTAL ,  {{{x^2+(1/(4pi))(10-4x)^2}}}
Or you put into what form you need.


MORE:  If you want as combined for same denominator then  {{{(4pi*x^2+(10-4x)^2)/(4pi)}}}.