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In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago

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Intern
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Joined: 15 Nov 2018
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Concentration: Finance, Entrepreneurship
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In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago  [#permalink]

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New post 14 Jan 2019, 11:18
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (03:01) correct 42% (02:55) wrong based on 44 sessions

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In the given figure ABCD is a rectangle and EFGHIJ is a regular hexagon. If the length of AD = 10cm then, find the area of the hexagon.


A) \(\frac{50}{√3}\)

B) \(50√3\)

C) \(100√3\)

D) \(100\)

E) \(100√3\)
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Re: In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago  [#permalink]

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New post 14 Jan 2019, 13:58
1
Someone please explain!

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Re: In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago  [#permalink]

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New post 14 Jan 2019, 15:51
2
1
Given EFGHIJ is a regular hexagon, we can conclude that
1) all sides are equal, which makes four triangles similar triangles, which means AJ=JD=BG=GC=10/2=5
2) each angle is 120 degrees. Which makes <AEJ, BFG, GHC, JID = 60 degrees.
Hence the four triangles are all 30-60-90 triangle, which follows the ratio of 1:√3:2
Let a=side of hexagon, we then get AJ/a=5/a=(√3)/2, a=10/(√3)

Area of a regular hexagon: (3√3)/2 * a^2
Sub in 10/(√3), A=50√3

B is correct.
GMAT Club Bot
Re: In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago   [#permalink] 14 Jan 2019, 15:51
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In the given figure ABCD is a rectangle and EFGHIJ is a regular hexago

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