The diagram below shows a rectangle inside a regular hexagon . the apothem of the hexagon is 19.05 units . to the nearest square unit . what is the area of the shaded region a. 1257 b.861 c.442 d.1653

Step-by-step explanation:

In the figure attached, you can observe that the shaded area can be found by calculating the difference between the area of the regular hexagon and the area of the rectangle inside.

The area of a regular hexagon is defined as

Where is the perimeter and is the apothem.

By given, we know that the side of the hexagon is 22 units.

Remember that the perimeter is the sum of all sides, in this case would be

.

The perimeter of the hexagon is 132 units.

Therefore, the area is

On the other hand, the area of the rectangle is defined as

, where is the base and is the height. We know, by given

Replacing these values, we have

As we said before, the shaded are is defined by the following difference

Replacing each area, we have

Therefore, the right answer is B. 861.

what are you trying to solve here

step-by-step explanation:

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