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Hexagon

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by rahulvsd » Tue Nov 08, 2011 7:23 pm
The hexagon has a center A and the length of AB is 4. What is the perimeter of this hexagon?

(1) The hexagon is a regular hexagon.

(2) The length of the top side is 4.

[spoiler]OA: A. What is top side?[/spoiler]
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Source: — Data Sufficiency |
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by user123321 » Tue Nov 08, 2011 8:11 pm
rahulvsd wrote:The hexagon has a center A and the length of AB is 4. What is the perimeter of this hexagon?

(1) The hexagon is a regular hexagon.

(2) The length of the top side is 4.

[spoiler]OA: A. What is top side?[/spoiler]
should be A.
1) In a regular hexagon, all sides are same and distance between centre A and vertex B is same as length of side => perimeter = 6*4 = 24. hence sufficient.
2) If one side of a hexagon is 4, we cannot say anything about the length of other sides, because it is not regular. And so perimeter cannot be determined. hence insufficient.

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by pemdas » Tue Nov 08, 2011 8:39 pm
in st(1) here it's very easy to determine that we have 120` angle @ internal angle for the regular hexagon (meaning all sides are equal) - the direct reference to memorized rules/theories of regular ***gons is not required
the formula applied (n-2)*180, n is number of sides in the regular polygon <> (6-2)*180=720.
720/6=120` is internal angle at each axis. Since angle @ axis (120`) is divided into 2 equal angles by the line connecting the hexagon's axis and its center, we have 60` at the base AB and other side with the central angle 360/6=60. We have equilateral triangle with all sides equal. Hence AB=side of hexagon.
rahulvsd wrote:The hexagon has a center A and the length of AB is 4. What is the perimeter of this hexagon?

(1) The hexagon is a regular hexagon.

(2) The length of the top side is 4.

[spoiler]OA: A. What is top side?[/spoiler]
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