# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Geometry Questions | Question 15

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Question 15 : 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

1. 3√2
2. 3
3. 4
4. √3

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##### Method of solving this CAT Question from Geometry

Given that ABCDEF be a regular hexagon with each side of length of 1 cm.
We have to find the area of a square with AC as one side.
ABO is the equilateral triangle with each side having length of 1 cm and ABCO is the rhombus.
Altitude of an equilateral triangle = $$frac{√3}{2}$ a So AP = $\frac{√3}{2}$ × 1 Where AP = PC ⟹ AC = AP + PC ⟹ AC = $\frac{√3}{2}$ × 2 ⟹ AC = √3 Area of a square = a2 sq.units Area of the square with AC as one side = √3 × √3 = 3 sq.units The question is "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"

##### Hence, the answer is 3

Choice B is the correct answer

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