JEE Main 2019 — Rotational Motion Question with Solution

An equilateral triangle $\mathrm{ABC}$ is cut from a thin solid sheet of wood. (See figure) $\mathrm{D},\mathrm{E}$ and $\mathrm{F}$ are the mid-points of its sides as shown and $\mathrm{G}$ is the centre of the triangle. The moment of inertia of the triangle about an axis passing through $\mathrm{G}$ and perpendicular to the plane of the triangle is ${\mathrm{I}}_0$. If the smaller triangle $\mathrm{DEF}$ is removed from $\mathrm{ABC}$, the moment of inertia of the remaining figure about the same axis is $I$. Then