CAT (QA) PYQs

Suppose the length of each side of a regular hexagon $ABCDEF$ is $2$ cm. It $T$ is the mod point of $CD$, then the length of $AT$, in cm, is

Corners are cut off from an equilateral triangle $T$ to produce a regular hexagon $H$. Then, the ratio of the area of $H$ to the area of $T$ is

Let $ABCDEF$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $AC$ as one side is