ABC is a plane lamina of the shape of an equilateral triangle. D, E...

Let mass of lamina $= m$, and length of side $= l$, then moment of inertila of lamina about an axis passing through $G$ and perpendicular to the plane.

${I}_{0} ∝ m{l}^{2}$

${I}_{0} = km{l}^{2}$

Let moment of inertila of $DEF = {I}_{1}$ about $G$

then, ${I}_{1} = \dfrac{{I}_{0}}{16}$

then,${I}_{ADE} = {I}_{BDF} = {I}_{EFC} = {I}_{2}$

$3{I}_{2} + {I}_{1} = {I}_{0}$

$3{I}_{2} + \dfrac{{I}_{0}}{16} = {I}_{0}$

$⇒$ ${I}_{2} = \dfrac{5{I}_{0}}{16}$

So, Moment of inertila of $DECB = 2{I}_{2} + {I}_{1}2\left(\dfrac{5{I}_{0}}{16}\right) + \left(\dfrac{{I}_{0}}{16}\right)$

$= \dfrac{11{I}_{0}}{16}$