The ratio of the sides of a rectangle and a regular hexagon is 4 : 3. The ratio of their areas is____________.

Correct option is A

Given:
The ratio of the side of a rectangle to the side of a regular hexagon is 4 : 3.
Let the side of the rectangle (assumed square) = 4x.
Let the side of the regular hexagon = 3x.
Formula Used:
Area of a square = side²
Area of a regular hexagon = $$\frac {3\sqrt 3}{ 2}$$​ × side²
Solution:
Area of rectangle (square) = (4x)² = 16x²
Area of regular hexagon = $$\frac {3\sqrt 3}{ 2}$$​ × (3x)² =$$\frac {3\sqrt 3}{ 2}$$​× 9x² = $$\frac {27\sqrt 3}{ 2}$$​x²
Now, the ratio of the areas (Rectangle : Hexagon) => 16x² : ($$\frac {27\sqrt 3}{ 2}$$​)x² = 32 : 27$$\sqrt 3$$​
Therefore, the ratio of their areas is 32 : 27$$\sqrt 3$$​