Distance around a shape is called the Perimeter. I hope I've helped in some way, shape or form!
We know that
if Anita divided a circle into 6 equal parts------> (1/6)+(1/6)+(1/6)+(1/6)+(1/6)+(1/6)
each part is --------> (1/6)
if shades 1 of the parts ----------> the part that she shaded is 1/6
the answer is (1/6)
Area of sector=sectorfraction times area
sector fraction=angle/360
area=pir^2
r=10
area=pi10^2=100pi
so
5pi/100pi=xdeg/360
1/20=x/360
times both sides by 360
18=x
answer is 18 degres