Question 1141838
A way to start is like this:
x, the amount to make the square
20-x, the amount to make the circle.


Area of Square:  {{{(x/4)^2=x^2/16}}}


Area of Circle:  circumference with radius r,  {{{2pi*r=20-x}}
meaning {{{r=(20-x)/(2pi)}}}
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Area of this part, {{{(20-x)^2/(4pi)}}}


A, the total area of combined square and circle:
{{{highlight_green(A=x^2/16+(20-x)^2/(4pi))}}}
This function is what you want to find the minimum for.   


The differentiation and algebraic steps should give 
{{{highlight_green(dA/dx=((8+pi)x-160)/(8pi)=0)}}}
and solving for x should be no trouble.