What I did:

r, radius of circle

d, diameter of circle

NOTE: diameter is also diagonal of square, therefore base of a triangle that is half of the square...

If you split the square into 2 triangles, they each have a height of r and a base of 2r...so...

A_{tri} = 1/2(r)(2r) = r^{2}

A_{square} = 2(r^{2}) = 2r^{2}

We know the area of the circle must be 3.14r^{2}

Now...to find the area of the circle outside the square we do: 3.14r^{2}
- 2r^{2} = 1.14r^{2}

To find the percent of the original circle that is, I think we do: __1.14r__^{2}
= .3630573

3.14r^{2}

That rounds to about 36.3%, or 36% I guess...I think this should work...she explained the triangles thing...