Question 936272
The rectangle would be a square.  The diagonal of the square is a diameter of the circle.  One diagonal cuts the square into two 45-45-90 special triangles.


circle, area  {{{pi*r^2}}}


The diagonal and diameter, {{{2r}}}.
Let x be the side length of one side of the square.
{{{x^2+x^2=(2r)^2}}}
and a picture would help you to see that.


{{{2x^2=4r^2}}}
{{{x^2=2r^2}}}
{{{x=r*sqrt(2)}}}


Area of the square:  {{{r^2*2}}}, and area of the circle was {{{pi*r^2}}}.
Percentage?
{{{highlight(100*(2/pi))}}}