Answer: The correct option is (A). 464 square units.
Step-by-step explanation: We are given a rectangle inside a regular hexagon in the figure.
We know that each side of a regular hexagon has same measure, so the measure of each side is
a = 18 units.
Therefore, the area of the regular hexagon is given by
[tex]A_h=\dfrac{3\sqrt3}{2}a^2=1.5\times 1.732\times 18^2=841.752~\textup{sq. units.}[/tex]
Since the rectangle has length and breadth of 21 units and 18 units respectively, so the area of the rectangle is
[tex]A_r=21\times 18=378~\textup{sq. units.}[/tex]
Thus, the area of the shaded region in the figure will be
[tex]A_h-A_r=841.752-378=463.752\sim 464~\textup{sq. units.}[/tex]
Hence, option (A) is correct.
