Let #r# be the inradius of the triangle,
given that the area of the incircle #=163pi#,
#=> pir^2=163pi#
#=> r=sqrt163#
Formula for inradius (#r#) of a triangle : #r=(2A)/p#,
where #A and p# are the area and the perimeter of the triangle, respectively.
Recall that area #A# of an equilateral triangle is : #A=(sqrt3a^2)/4#,
where #a# is the side length of the equilateral triangle.
#=> r=(2A)/p=((2*sqrt3a^2)/4)/(3a)=(sqrt3a)/6#
#=> (sqrt3a)/6=sqrt163#
#=> a=(6sqrt163)/sqrt3=2sqrt489# units
Footnotes: formula for inradius #r# of an equilateral traingle is given by :
#r=sqrt3/6a#,
where #a# is the side length of the equilateral triangle.
