Find the area of the square in the figure.

The equation of a circle centered on origin is
x²+y²=r² where r is the radius, so r²=16 in our equation so the radius of the circle is 4
we now have a total of 8 45-45 right triangle with hypotenuse 4. a 45-45 right triangle with hypotenuse 4 has legs of length 2√2. our big square is then 4√2 on a side. square this to get the squares area, which is 32