In the given figure, ABCDEF is a regular hexagon whose side is 12 cm. What is the shaded area (in cm²)?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Area of }}\Delta {\text{BIC}} = \frac{{\sqrt 3 }}{4} \times 12 \times 12 = 36\sqrt 3 \cr & {\text{Area of }}\Delta {\text{BIA}} = 36\sqrt 3 \cr & {\text{Area of }}\Delta {\text{BGI}} = \frac{{36\sqrt 3 }}{2} = 18\sqrt 3 \cr & {\text{Area of shaded region}} \cr & = 36\sqrt 3 + 18\sqrt 3 \cr & = 54\sqrt 3 {\text{ c}}{{\text{m}}^2} \cr} $$