Area of any polygon =
r×s(where r is the inradius and s is the semiperimeter)
Hence, for any n sided regular polygon with inradius r and side x units,
Area
=(nx)×rSince the area is given as 10x sq units
×n×x×r=10x⇒
n×r=20Here n must be more than or equal to 3.
So the possible values of (n, r) are (4, 5), (5, 4), (10,2), and (20,1).