Question 237226
The circle has a diameter of 10 cm.  Let x= length of the side of the square.  Draw the circle of diameter 10, showing the square with side of x inside the circle.  You will see a right triangle, so by Theorem of Pythagoras 


{{{x^2 + x^2 = 10^2}}}

{{{2x^2= 100}}}

{{{x^2 = 50}}}


Now this looks ugly, but remember that all you need to find is the AREA of the square.  The area is {{{x^2}}}, so this is the answer to the question:  


Area = {{{x^2}}}=50 sq cm.


Dr. Robert J. Rapalje