Question 486247
The area of your big square will be the side of the square squared, so if the area of your big square is 4a^2, a side will be 2a.

You are correct in that this is also the diameter of the circle.

You are correct that this will be the hypotenuse of  triangle formed from  the inner square (2a).
What is formed by the diagonal of the circle, is two 45 45 90 degree triangles, we need to find the length of the sides; after which we can determine the area of the inner triangle.

In a 45 90 45 triangle, the sides are s and the hypotenuse is s{{{sqrt(2)}}}
Therefore 2a = s{{{sqrt(2)}}}.
Worked out, s = (2a{{{sqrt(2)}}})/2.
To find the area of the inner square we will square (2a{{{sqrt(2)}}})/2.
We obtain 2A^2.
Cleomenius.