Let ABCDEF be a regular hexagon with each side of length 1 cm

• Mensuration

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

Answer

In ∆ABC, AB = 1 cm, BC = 1 cm and ∠B = 120°

Draw perpendicular BO from B to AC. So, in right triangle AOB 

cos 30° = AO/AB = AO/1

AO = √3/2

Similarly, OC = √3/2

AC = AO + OC = √3/2 + √3/2 = √3

The square of side √3 cm will have an area of (√3)² = 3 cm² 

The correct option is B.