Side of a hexagon is 4 cm. Side of a square is $4\sqrt{2}$ cm. What is the ratio of their areas?

$3\sqrt{3}:4$

Side of a hexagon = 4 cm

Side of a square = 4\(\sqrt {2}\)cm

 Area of hexagon = \(\frac{3}{2}\)\(\sqrt {3}\)(side)²

So, according to the question,

Area of hexagon =  \(\frac{3}{2}\)\(\sqrt {3}\)(4)²= 24\(\sqrt {3}\)

Area of the square = (4\(\sqrt {2}\))² = 32 cm²

Area of hexagon: Area of the square = 24\(\sqrt {3}\) : 32 = 3\(\sqrt {3}\) : 4