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# If all sides and angles of the hexagon inscribed in the circle above w

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
If all sides and angles of the hexagon inscribed in the circle above w  [#permalink]

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09 Sep 2018, 06:56
00:00

Difficulty:

15% (low)

Question Stats:

87% (01:14) correct 13% (02:02) wrong based on 19 sessions

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If all sides and angles of the hexagon inscribed in the circle above with center O are the same and the radius if the circle is 1, what is the area of the hexagon?

A. $$\frac{3\sqrt{3}}{2}$$

B. 3

C. $$3\sqrt{3}$$

D. 6

E. $$6\sqrt{3}$$

Attachment:

image005.jpg [ 1.88 KiB | Viewed 387 times ]

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Joined: 11 Sep 2015
Posts: 3440
Re: If all sides and angles of the hexagon inscribed in the circle above w  [#permalink]

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09 Sep 2018, 07:30
Top Contributor
Bunuel wrote:

If all sides and angles of the hexagon inscribed in the circle above with center O are the same and the radius if the circle is 1, what is the area of the hexagon?

A. $$\frac{3\sqrt{3}}{2}$$

B. 3

C. $$3\sqrt{3}$$

D. 6

E. $$6\sqrt{3}$$

Attachment:
image005.jpg

If all of the sides are equal, then each of the central angles is 60°

Since each radius is 1, then we can see that the hexagon is composed of 6 EQUILATERAL triangles

Useful formula:
Area of an equilateral triangle = (side²)(√3/4)
Each side has length 1, so the area of ONE triangle = (1²)(√3/4) = √3/4

Since there are 6 equilateral triangles in the hexagon, the TOTAL area = 6(√3/4) = (6√3)/(4) = (3√3)/(2)

Cheers,
Brent
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Re: If all sides and angles of the hexagon inscribed in the circle above w   [#permalink] 09 Sep 2018, 07:30
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