|
|
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.
03 Apr 2020, 04:21
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:43) correct
24%
(01:34)
wrong
based on 41
sessions
History
Date
Time
Result
Not Attempted Yet
Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
A. √3
B. 3
C. 4
D. 3√2
E. 8
Are You Up For the Challenge: 700 Level Questions
A. √3
B. 3
C. 4
D. 3√2
E. 8
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 04:46
Kudos
Bookmarks
Bunuel
Formula: Each interior angle in an n-sided regular polygon = \(\frac{180(n - 2)}{n}\)
For regular hexagon, Each interior angle = \(\frac{180(6 - 2)}{6} = 120\)
Triangle ABC is isosceles with angles (30, 30 ,120)
--> Ratio of sides AB : BC : AC = \(1 : 1 : \sqrt{3}\)
Given, AB = BC = \(1\). So, AC = \(\sqrt{3}\)
--> Area of square with side AC = \((\sqrt{3})^2 = 3\)
Option B
Attachments
2.JPG [ 16.74 KiB | Viewed 14311 times ]
03 Apr 2020, 05:47
Kudos
Bookmarks
Bunuel
Solution:
- o ABCDEEF is a regular hexagon
- o Every sides of the hexagon are equal.
o Every angles of the hexagon are equal.
- o We know that ∠ABC = 120 [ABCDE is regular hexagon.]
- o ∠ABM = 60 [BM is perpendicular on AC]
- o \(BM: AM: AB = 1: \sqrt{3}: 2\)
- \(\frac{AM}{AB} = \frac{\sqrt{3}}{2}\)
\(\frac{AM}{1} = \frac{\sqrt{3}}{2}\)
\(AM =\frac{\sqrt{3}}{2}\)
o Area of the square = \((\sqrt{3})^2 = 3\)
