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# ABCDEF is a regular hexagon inscribed inside a circle.

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Intern
Joined: 16 Apr 2017
Posts: 45
ABCDEF is a regular hexagon inscribed inside a circle.  [#permalink]

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21 Jul 2017, 10:41
5
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Difficulty:

55% (hard)

Question Stats:

56% (02:22) correct 44% (02:57) wrong based on 18 sessions

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ABCDEF is a regular hexagon inscribed inside a circle. If the shortest diagonal of the hexagon is of length 3 units, what is the area of the shaded region.
1) 1/6(3Π − (9√3)/2)
2) 1/6(2Π − (6√3)/2)
3) 1/6(3Π − (8√3)/2)
4) 1/6(6Π − (15√3)/2)
5) 1/6(6Π − (13√3)/2)

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Joined: 05 Feb 2017
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Re: ABCDEF is a regular hexagon inscribed inside a circle.  [#permalink]

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21 Jul 2017, 11:24
A is the correct answer.
There is a trick.
Each of the small diagonal of hexagon is 2*side*(root3)/2.
Each of the large diagonal in the same way is 2*side.
So here put this formula =3 .You will get side as 6/2(root3) which is ultimately the radius .Solve and you will get A

1/6pie(r^2)-((root3)/4)r^2

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ABCDEF is a regular hexagon inscribed inside a circle.  [#permalink]

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Updated on: 23 Jul 2017, 06:03
Supermaverick wrote:
ABCDEF is a regular hexagon inscribed inside a circle. If the shortest diagonal of the hexagon is of length 3 units, what is the area of the shaded region.
1) 1/6(3Π − (9√3)/2)
2) 1/6(2Π − (6√3)/2)
3) 1/6(3Π − (8√3)/2)
4) 1/6(6Π − (15√3)/2)
5) 1/6(6Π − (13√3)/2)

Attachment:

reg.hex-in-circle.jpg [ 105.54 KiB | Viewed 5180 times ]

Answer A. From the figures, just a few things to note:

1. Short diagonal BD = 3 is also the side opposite a 30-60-90 triangle created by bisection of regular hexagon's 120 degree angle

2. I used that side to figure side AB, which is also radius. (I got that they're equal; just draw imaginary line from my figure's center to B . . . just thought I ought to keep the diagram as simple as possible.)

3. I didn't show calculations, and assumed some things would be obvious, e.g. diameter AD = 2r. I did show formulas and values. The math isn't hard. Just painstaking. I think I'm shell-shocked.
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Originally posted by generis on 22 Jul 2017, 13:11.
Last edited by Bunuel on 23 Jul 2017, 06:03, edited 1 time in total.
Edited.
Intern
Joined: 10 Nov 2018
Posts: 23
Re: ABCDEF is a regular hexagon inscribed inside a circle.  [#permalink]

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17 May 2019, 02:08
I think the diameter will be 2 Root 3 and not 3 root 3.

As all calculations are based on 2 root 3.
Re: ABCDEF is a regular hexagon inscribed inside a circle.   [#permalink] 17 May 2019, 02:08
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# ABCDEF is a regular hexagon inscribed inside a circle.

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