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655-705 (Hard)|   Geometry|      
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rahuliit2003
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Find the area of regular hexagon H. 02 May 2019, 03:35
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

49% (01:33) correct 51% (01:20) wrong based on 38 sessions

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Find the area of the regular hexagon R.

(1) A circle of radius A units is inscribed in the hexagon.
(2) Each side of the hexagon subtends 60 degrees at the center of R.

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Is the answer A or E?
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E
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anothermillenial
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Find the area of regular hexagon H. 02 May 2019, 03:53
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rahuliit2003
Find the area of the regular hexagon R.

(1) A circle of radius A units is inscribed in the hexagon.
(2) Each side of the hexagon subtends 60 degrees at the center of R.

Is the answer A or E?

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A
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A. If you know the radius of the circle, the rest is basically 6*area of equilateral triangle, which we can calculate. Statement (2) is basically repeating what we know about hexagons.
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nick1816
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Find the area of regular hexagon H. 02 May 2019, 07:39
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Statement 1-
side of regular hexagon= 2* radius of inscribed circle in hexagon= 2A
Area of regular Hexagon= [3*(3^1/2)* (2A)^2]/2
Sufficient
Statement 2
Each side of any regular hexagon subtends 60 degrees at the center of that hexagon
We have no clue about the length of hexagon, hence it's impossible to find the area
Insufficient
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Find the area of regular hexagon H. 02 May 2019, 09:27
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rahuliit2003
Find the area of the regular hexagon R.

(1) A circle of radius A units is inscribed in the hexagon.
(2) Each side of the hexagon subtends 60 degrees at the center of R.

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Is the answer A or E?
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Straight E. There is no values hinted in the question

statement 1: since A is unknown, so Insufficient.
but here are the formulas if A is Known:
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if a circle is inscribed in a regular hexagon, then side \(S = \frac{2r}{\sqrt{3}}\)
area of regular hexagon is \(\frac{3*\sqrt[]{3}}{2}S^2\)
so Area of the Hexagon is \(\frac{3*\sqrt[]{3}}{2}(\frac{2A}{\sqrt{3}})^2\) = \(2\sqrt{3}A^2\)
Statement 2: if "Each side of the hexagon subtends 60 degrees at the center of R", then the hexagon is Regular (no additional info) --> Insufficient
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Find the area of regular hexagon H. 03 May 2019, 08:46
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You'll never see a question like this one on the GMAT. To answer the question, we have to know the value of the radius.
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