Question 553370
Area of a circle:  {{{A= pi*r^2}}}


If r=1, then {{{A=pi*1^2=pi}}}


Area of a semicircle {{{A=(pi*r^2)/2}}}


Since the area of the semicircle is the same as the area of the circle, {{{A=pi}}}.


{{{pi = (pi*r^2)/2}}}


Multiply both sides by 2 to clear the fraction:
{{{2pi= pi*r^2}}}


Divide both sides by pi:

{{{2= r^2}}}


{{{r^2=2}}}
{{{r=sqrt(2)}}} or {{{r=-sqrt(2)}}}  Reject the negative answer since a radius cannot be negative.


{{{r=sqrt(2)}}}  Final Answer!!



Happy New Year!! My Email address is rapaljer@seminolestate.edu if you need to contact me!! 


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