A room is in the shape of cube and the length of the longest rod placed in it is $21\sqrt{3}$cm. The area of the floor is:

441 cm²

We know that,

Diagonal of cube = Side\(\sqrt {3}\)

Area of floor = Side²

We have,

Length of the longest rod = 21\(\sqrt {3}\) m.

Length of the longest rod of cube = Diagonal of cube = \(\sqrt {3}\) × Side of cube

21\(\sqrt {3}\) = Side\(\sqrt {3}\)

Side = 21 m

Area of floor = = 21²  = 441 m².