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

A (APEX)

Explanation:

Answer 2

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=(3\sqrt3)/(2)a^2=1.5* 1.732* 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* 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.