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) 6 sqrt 2 cm^ 2 B) 6 sqrt 3 cm^ 2 C) 12sqrt(2c) * m ^ 2 D) 12 sqrt 3 cm^ 2
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Step-by-step explanation:
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×(2)
2
×
4
3
=12
3
cm
2
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