Solution: A regular hexagon can be divided into 6 equilateral triangles, each with side length 3 cm. The area of one equilateral triangle is $\frac\sqrt34 \times 3^2 = \frac9\sqrt34$. The total area is $6 \times \frac9\sqrt34 = \frac54\sqrt34 = \frac27\sqrt32$. - Veritas Home Health