Question 599110
This square is inscribed in the circle of radius 6. So the diagonal of the square is 2*6 = 12 cm



Let x = length of the side of the square



So by the pythagorean theorem


a^2 + b^2 = c^2


x^2 + x^2 = 12^2


2x^2 = 144


x^2 = 144/2


x^2 = 72


x = sqrt(72)


x = 6*sqrt(2)



So the length of the side of the square is 6*sqrt(2) cm



Now use it in the area for a square formula


A = s^2


A = (6*sqrt(2))^2


A = (6*6)*(sqrt(2)*sqrt(2))


A = 36*sqrt(4)


A = 36*2


A = 72


So the area of the square is 72 square cm.