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03 Apr 2020, 04:21
Kudos
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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
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Time
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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
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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 = \((\sqrt{3})^2 = 3\)
