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

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Director
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given figure is that of a regular hexagon. what is the area? [#permalink] New post 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] New post 30 Jan 2018, 07:10
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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
[Reveal] Spoiler:
\(96*\sqrt{3}\)


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

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

Answer: 96√3

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Brent
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Re: given figure is that of a regular hexagon. what is the area? [#permalink] New post 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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