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# given figure is that of a regular hexagon. what is the area?

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given figure is that of a regular hexagon. what is the area? [#permalink]  30 Jan 2018, 00:05
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given figure is that of a regular hexagon. what is the area of the hexagon? Give your answer without the units
[Reveal] Spoiler:
$$96*\sqrt{3}$$

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Re: given figure is that of a regular hexagon. what is the area? [#permalink]  30 Jan 2018, 07:10
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Expert's post
amorphous wrote:
given figure is that of a regular hexagon. what is the area of the hexagon? Give your answer without the units
[Reveal] Spoiler:
$$96*\sqrt{3}$$

Notice that we can divide a regular hexagon into 6 identical equilateral triangles

So, area of hexagon = 6(area of 1 equilateral triangle)

Useful formula: Area of equilateral triangle = (side²)(√3)/4

Since each side has length 8, we can write: Area of one equilateral triangle = (8²)(√3)/4
= (64)(√3)/4
= 16√3

So, area of hexagon = 6(area of 1 equilateral triangle)
= area of hexagon = 6(16√3)
= 96√3

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: given figure is that of a regular hexagon. what is the area? [#permalink]  30 Jan 2018, 07:43
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amorphous wrote:
given figure is that of a regular hexagon. what is the area of the hexagon? Give your answer without the units

Here we know

Area of Hexagon = $$[3\sqrt{3} * (side)^2]$$$$/2$$

since side = 8

Therefore putting the value in the equation we get= $$[3\sqrt{3} * (8)^2]$$$$/2$$
= $$96\sqrt{3}$$
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Re: given figure is that of a regular hexagon. what is the area?   [#permalink] 30 Jan 2018, 07:43
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