Question 1177700

*[illustration semicircle.png].

refer drawing , the side of the square on the diameter is symmetric from the centre, 
sides of square are 2x each,  The diagonal is the radius, = 5 cm. It is a right triangle.
x^2+(2x)^2=5^2=25 ( Pythagoras theorem)

 
5x^2=25
x^2=5
x= sqrt(5) cm.
2x= 2sqrt(5) cm.
The area of the square is  {{{(2(sqrt(5)))^2=4*5=20 cm^2}}}