Question : The area of a regular hexagon with side '$a$' is:
Option 1: $\frac{3\sqrt3}{4}a^2$ sq. unit
Option 2: $\frac{12}{2\sqrt3}a^2$ sq. unit
Option 3: $\frac{9}{2\sqrt3}a^2$ sq. unit
Option 4: $\frac{6}{2\sqrt3}a^2$ sq. unit
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Correct Answer: $\frac{9}{2\sqrt3}a^2$ sq. unit
Solution :
If we break a regular hexagon with side '$a$', then we will get 6 equilateral triangles with sides '$a$'.
So, the area of a regular hexagon = 6 × (Area of an equilateral triangle)
We know that, the area of an equilateral triangle with side '$a$' = $\frac{\sqrt3}{4}a^2$
Therefore, the area of the regular hexagon with side '$a$'
= $6×\frac{\sqrt3}{4}a^2$
= $\frac{3\sqrt3}{2}a^2$
= $\frac{9}{2\sqrt3}a^2$
Hence, the correct answer is $\frac{9}{2\sqrt3}a^2$ sq. unit.
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