Answer
Please see the work below.
Work Step by Step
We know that
(a) The distance from the center of the vertices is given as:
$d=\frac{1}{\sqrt{3}}$
We know that the rotational inertia is given as
$I=3(md^2)=3(m(\frac{L}{\sqrt{3}})^2)=mL^2$
(b) We know that
$I=2m(\frac{L}{2})^2=(\frac{1}{2})mL^2$
