Question 1008887
find the number of sides of a regular polygon whose sides measure half of its apothem.
we know that
Apothem=s/2tan(180/n)   where s = length of side  n is number of side 
as per given condition Apothem is half of side =s/2
s/2=s/2tan(180/n)   cancelling s and 2 both side 
1=tan(180/n)
tan 45=tan(180/n)
45=180/n
n=180/45=4
so it is having 4 side
short cut 
if apothem is half of side of regular polygon  than center angle will be 90 degree
90=860/n
n=360/9= 4 side  it means it is rhombus