What happens to the area of the square when its side is halved?

area = side x side

if the side is halved, then

new_area = side/2 x side/2

= side x side / 4

= area / 4

The area becomes a quarter of what is was.

With similar objects,

The ratio of areas is the square of the ratio of the lengths

The ratio of volumes is the cube of the ratio of the lengths.