Question

“The diagram below shows a rectangle inside a regular hexagon. The apothem of the hexagon is 15.59 units. To the nearest square unit, what is the area of the shaded region?

Answer 1

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

$A_h=\dfrac{3\sqrt3}{2}a^2=1.5\times 1.732\times 18^2=841.752~\textup{sq. units.}$

Since the rectangle has length and breadth of 21 units and 18 units respectively, so the area of the rectangle is

$A_r=21\times 18=378~\textup{sq. units.}$

Thus, the area of the shaded region in the figure will be

$A_h-A_r=841.752-378=463.752\sim 464~\textup{sq. units.}$

Hence, option (A) is correct.

Answer 2

Answer:

A (APEX)

Step-by-step explanation: