Question 731997
{{{drawing(300,300,-5,5,-5,5,
rectangle(-4,-4,4,4),
circle(0,0,4),
rectangle(-2sqrt(2),-2sqrt(2),2sqrt(2),2sqrt(2)),
line(-4,4,4,-4),
line(2sqrt(2),-2sqrt(2),-2sqrt(2),2sqrt(2)),
line(-4,0,4,0)
)}}} If the measure of the side of the small square is {{{a}}}, its area is {{{a^2}}} .
The Pythagorean theorem says that the diagonal of the small square is {{{a*sqrt(2)=sqrt(a^2+a^2)=sqrt(2a^2)}}}.
Since that is the diameter of the circle, and the side of the large square,
the area of the large square is {{{(a*sqrt(2))^2=2a^2}}}
Then, the ratio of the areas is {{{2a^2/a^2=highlight(2)}}} .