Question 223686
If the radius of the semicircle is 8, then the circumference of the entire circle is {{{C=2*pi*r=2*pi*8}}}. 


Since it's a semicircle, take half of this, and add in a diameter of 16, and you get the perimeter of the semicircle is {{{pi*8+16}}} 


Let x = side of the square, which has a perimeter of 4x.


Since the perimeter of the square equals the perimeter of the semicircle,
{{{4x=8*pi+16}}}


Divide both sides by 4:
{{{x=2*pi +4}}}


R^2


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus