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

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

Answer: Option A

Solution

Answer: Option A

Solution:

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