Quantitative Aptitude – Geometry – Polygons – Let ABCDEF be a regular hexagon
Quantitative Aptitude – Geometry – Polygons
Question
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√2
B) 3
C) 4
D) √3
Answer
Option (B)
Solution
From CAT 2017 – Quantitative Aptitude – Geometry – Polygons, we can see that,
Angle (ABC) = 120 deg
According to the formula,
Cos (theta) = (b^2 + c^2 – a^2)/2bc
Cos (120) = [(AB)^2 + (BC)^2 – (AC)^2]/2*AB*BC
-1/2 = [1+1 – (AC)^2]/2
=> On solving, we get, AC = √3
Area of square = (side)^2 = (√3)^2 = 3
Option B is the right answer.
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