```Question 478522
The first thing I did was to find the side of the square inscribed in the circle,
as the diameter of the circle will be the diagonal of the square, this will form  two  45 45 90 right triangles with a hypotenuse of 2.

Since s = ssqrt(2), 2  = s(sqrt(2).
divide 2 by sqrt(2) = 2/sqrt(2)
Multiply the numerator and denominator by sqrt(2) to obtain 2(sqrt(2)/2 for each side of the square, or sqrt(2)

Now, these are being used as diameters  for four more circles, so we determine the radius of each one of the four to be sqrt(2)/2

So this value squared times pi will be the area of each circle, or 2/4 = 1/2 times pi = 1/2 pi for each circle times four circles results in 2 pi as the area for the four circles combined.

The area of the original circle is pi r^2, radius being 1 so the area of the original circle will come to 1pi.

So, since the outer circles obviously cover the original circle completely, the area outside the original should be 2pi minus pi, or one pi.

Cleommenius.

```