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Find the area of a regular hexagon if the apothem is 8sqrt3 m, and a side is 16m. Round to the nearest whole number.
Answer options: 998, 665, 222, 1330

Find the area of a regular hexagon if the apothem is 8sqrt3 m and a side is 16m Round to the nearest whole number Answer options 998 665 222 1330 class=

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carlosego

Answer: SECOND OPTION.

Step-by-step explanation:

To calculate the area of the regular hexagon you must apply the following formula:

[tex]A=\frac{P*a}{2}[/tex]

Where P is the perimeter and a is the apothem.

The perimeter is:

[tex]P=6*s[/tex]

Where s is the lenght of a side.

Then:

 [tex]P=6*16m=96m[/tex]

Then, the area is:

[tex]A=\frac{96m*8\sqrt{3}m}{2}\\A=665m^{2}[/tex]

Answer:

Option 2. 665 m² is the correct answer.

Step-by-step explanation:

It has been given in the hexagon apothem is 8√3 and one side of the hexagon is 16 m.

We have to calculate the area of regular hexagon.

Area of hexagon = 6 × area of a triangle formed with one side of hexagon.

                           = 6 × 1/2( Base × height)

                          = 3 × (8√3 × 16)

                          = 384√3 = 665 m²

So the answer is 665 m².

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