5. A square and a regular hexagon are drawn with the same side length. If the area of the square is $\sqrt{3}$, what is the area of the hexagon?
Solution: The hexagon is composed of six equilateral triangles each of side length $\sqrt[4]{3}$ (with base $b=\sqrt[4]{3}$ and height $\frac{\sqrt{3}}{2} b$ ), so the total area is $\frac{9}{2}$.