<Tr> <Td> A filled regular hexagon with a side length of a </Td> <Td> </Td> <Td> I x = 5 3 16 a 4 (\ displaystyle I_ (x) = (\ frac (5 (\ sqrt (3))) (16)) a ^ (4)) I y = 5 3 16 a 4 (\ displaystyle I_ (y) = (\ frac (5 (\ sqrt (3))) (16)) a ^ (4)) </Td> <Td> The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin . </Td> </Tr> <P> The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of mass and the perpendicular distance (d) between the axes . </P> <P> I x ′ = I x + A d 2 (\ displaystyle I_ (x') = I_ (x) + Ad ^ (2)) </P>

Moment of inertia of quarter circle about centroidal axis