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CAT 2017 Slot 2 — QA Question 15

HexagonEasy

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

Answer & solution

  • A

    3√2

  • 3

  • C

    4

  • D

    √3

Solution

ABCDEF is a hexagon with side 1 cm. Let us construct the diagram as shown below

Now if we look at triangle ABC 

Further, as AB = BC, △ABC will become a 120° - 30° - 30° triangle and the ratio of it’s sides. (∵ ∠ABC is an angle of regular hexagon ABCDEF)

will be √3 : 1 : 1.

Now ACAB=31

∴ AC = √3 units

Area of square with side AC = (√3)2 = 3 sq.units

Hence, option (b).

CAT 2017 Slot 2 QA Q15: 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 — Solution | TheCATExam