Answer
$.29 \ kgm^2$
Work Step by Step
Recall, the moment of inertia is equal to the sum of the moments of inertia of every aspect of the object, including the masses. Thus, we find:
$I = m(\frac{1}{4}L)^2 + m(\frac{3}{4}L)^2 = \frac{5mL^2}{8}= \frac{5(.64)(.85)^2}{8}= .29 \ kgm^2$