Question

The sides of a regular hexagon of length 2 cm are extended The alternate sides meet in 6 new points the area of the star-shaped region so obtained is ___________

• A. $12\sqrt{3}c{m}^2$
• B. $6\sqrt{2}c{m}^2$
• C. $6\sqrt{3}c{m}^2$
• D. $12\sqrt{2}c{m}^2$

Answer 1

The correct option is A $12\sqrt{3}c{m}^2$

The extended alternate side forms a triangle with the included side of the hexagon.

It's a equilateral triangle with side 2 cm.

So we have such 6 equilateral triangles in the star.

The area of the star shaped region = Area of hexagon + area of 6 equilateral triangles

= 2 x 6 x Area of one equilateral triangle,

= $12\times (2{)}^2\times \sqrt{\frac{3}{4}}=12\sqrt{3}c{m}^2$