Exact area of a regular hexagon from sine 60 degrees

Do not use a calculator in this question.

1. By drawing the perpendicular from one vertex of an equilateral triangle of side \(2\) units to the opposite side, show that \(\sin60^\circ=\dfrac{\sqrt{3}}{2}\).[2]
2. Hence show that the area of an equilateral triangle of side \(s\) is \(\dfrac{\sqrt{3}}{4}s^2\).[2]
3. Find the exact area of a regular hexagon of side \(6\) cm.[2]