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Igoryamba
3 years ago
6

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

Mathematics
2 answers:
gregori [183]3 years ago
8 0

Answer:

<h2>B. 861.</h2>

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

A_{hexagon} =\frac{Pa}{2}

Where P is the perimeter and a 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

P_{hexagon}=22(6) =132.

The perimeter of the hexagon is 132 units.

Therefore, the area is

A_{hexagon} =\frac{132(19.05)}{2}=\frac{2514.6}{2}=1257.3 u^{2}

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

A_{rectangle}=bh, where b is the base and h is the height. We know, by given

b=22\\h=18

Replacing these values, we have

A_{rectangle}=bh=22(18)=396 u^{2}

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

A_{shaded}=A_{hexagon}-A_{rectangle}

Replacing each area, we have

A_{shaded}=A_{hexagon}-A_{rectangle}\\A_{shaded}=1257.3u^{2} -396u^{2}=861.3 u^{2}

Therefore, the right answer is B. 861.

Ulleksa [173]3 years ago
5 0
The correct answer is: B 861
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