Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
19 Aug 2013, 02:29
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
Hi Guys,
We all come across Hexagon questions and get stuck.
Here are below few concepts to help you tackle any Hexagon question.
Note: Please see the figure side by side to understand this concept clearly.
First of all, What is a HEXAGON??
Properties of HEXAGON:
No of sides - 6
No. of Diagonals - 9
Area of Hexagon- \(3\sqrt{3}a^2/2\) , where a is side of Hexagon.
Most people think that HEXAGON has only 3 diagonals( AD, BE and FC).
Well,This is absolutely incorrect.....
Lets prove it if you don't believe me..
The no. of diagonals of any polygon can deducted from nC2- n
=> 6C2 -6
=> 15 -6
=> 9
As shown in the figure,
HEXAGON has 9 Diagonals( 6 long diagonals and 3 small diagonals)
Long Diagonals- AC,CE,EA,BF,FD and DB
Small Diagonals- AD,BE and FC
SECRET BEHIND HEXAGON:
Hexagon basically consists of 6 similar equilateral triangles.
In the figure, the six triangles are AGF, AGB ,BGC, GDC, GED and FGE.
Lets assume "a" is the side of HEXAGON as shown in the figure.
Now, AG = GD = a [ since equilateral triangles share sides of equal length "a"]
The length of the any small diagonal will be 2a, i.e for AD,BE and FC.
For Long Diagonals, lets try to calculate the value.
In triangle AFG,
Let AO is perpendicular bisector,
AO=\(a\sqrt{3}/2\) [ the altitude in an equilateral triangle is \(a\sqrt{3}/2\)]
So FO=OG=a/2
Now, OC = a +a/2 => 3a/2
In right angle triangle AOC,
\(AC^2 = AO^2 + OC^2\) [ Pythagorum theorem]
\(AC^2 = 3a^2/4 + 9a^2/4\)
\(AC^2 = 12a^2/4\)
\(AC^2= 3a^2\)
\(AC = a\sqrt{3}\)
For any HEXAGON will side "a",
The length of any long diagonal is \(a\sqrt{3}\) , i.e for AC,CE,EA,BF,FD and DB
The length of any small diagonal is 2a, i.e for AD,BE and FC.
Area of polygon= Sum of Area of six equilateral triangles
=> \(6 * \sqrt{3}a^2/4\)
=> \(3\sqrt{3}a^2/2\)
Thanks,
Jai
KUDOS if it HELPED..!!!
We all come across Hexagon questions and get stuck.
Here are below few concepts to help you tackle any Hexagon question.
Note: Please see the figure side by side to understand this concept clearly.
First of all, What is a HEXAGON??
Attachment:
File comment: hexagon
hexagon.jpg [ 50.09 KiB | Viewed 13606 times ]
It is six dimensional regular polygon. hexagon.jpg [ 50.09 KiB | Viewed 13606 times ]
Properties of HEXAGON:
No of sides - 6
No. of Diagonals - 9
Area of Hexagon- \(3\sqrt{3}a^2/2\) , where a is side of Hexagon.
Most people think that HEXAGON has only 3 diagonals( AD, BE and FC).
Well,This is absolutely incorrect.....
Lets prove it if you don't believe me..
The no. of diagonals of any polygon can deducted from nC2- n
=> 6C2 -6
=> 15 -6
=> 9
As shown in the figure,
HEXAGON has 9 Diagonals( 6 long diagonals and 3 small diagonals)
Long Diagonals- AC,CE,EA,BF,FD and DB
Small Diagonals- AD,BE and FC
SECRET BEHIND HEXAGON:
Hexagon basically consists of 6 similar equilateral triangles.
In the figure, the six triangles are AGF, AGB ,BGC, GDC, GED and FGE.
Lets assume "a" is the side of HEXAGON as shown in the figure.
Now, AG = GD = a [ since equilateral triangles share sides of equal length "a"]
The length of the any small diagonal will be 2a, i.e for AD,BE and FC.
For Long Diagonals, lets try to calculate the value.
In triangle AFG,
Let AO is perpendicular bisector,
AO=\(a\sqrt{3}/2\) [ the altitude in an equilateral triangle is \(a\sqrt{3}/2\)]
So FO=OG=a/2
Now, OC = a +a/2 => 3a/2
In right angle triangle AOC,
\(AC^2 = AO^2 + OC^2\) [ Pythagorum theorem]
\(AC^2 = 3a^2/4 + 9a^2/4\)
\(AC^2 = 12a^2/4\)
\(AC^2= 3a^2\)
\(AC = a\sqrt{3}\)
For any HEXAGON will side "a",
The length of any long diagonal is \(a\sqrt{3}\) , i.e for AC,CE,EA,BF,FD and DB
The length of any small diagonal is 2a, i.e for AD,BE and FC.
Area of polygon= Sum of Area of six equilateral triangles
=> \(6 * \sqrt{3}a^2/4\)
=> \(3\sqrt{3}a^2/2\)
Thanks,
Jai
KUDOS if it HELPED..!!!
18 Sep 2021, 05:59
Kudos
Bookmarks
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
