# Triangle Inside a Hexagon

Geometry Level pending

$$ABCDEF$$ is a regular hexagon with $$CD = 1 \text{ cm}$$. Point $$H$$ lies on $$DE$$ such that $$DH = HE$$. Point $$G$$ lies on $$EF$$ such that $$EG = GF$$. Diagonal $$CF$$ intersects segment $$BG$$ at $$J$$ and intersects $$BH$$ at $$K$$. Find the area of $$\triangle BJK$$ (in $$\text{cm}^2$$) to two decimal places.