Question 1117326
the circumference of a circle is equal to 2 * pi * r


the circumference of half a circle is equal to pi * r + 2 * r.


you are talking about half the circumference of the circle plus the length of the diagonal which is equal to 2 * r.


the area of the circle is equal to pi * r^2.


the area of half the circle is equal to pi * r^2 / 2


if the circumference of half the circle is equal to the area of half the circle, then:


pi * r + 2 * r = pi * r^2 / 2


multiply both sides of this equation by 2 to get:


2 * pi * r + 4 * r = pi * r^2


divide both sides of this equation by r to get:


2 * pi + 4 = pi * r


divide both sides of this equation by pi to get:


(2 * pi + 4) / pi = r


that's your solution.


you have r = (2 * pi + 4) / pi.


this is the same as what you are showing, except that you needed to put parentheses around 2pi + 4.


what you are showing as 2π+4/π should be (2π+4)/π