Answer:
[tex]374.12\ cm^2[/tex]
Step-by-step explanation:
A regular hexagon is 6-sided polygon with all sides of equal length and all interior angles of equal measure. Each regular hexagon consists of 6 equilateral triangles formed by the center of hexagon and two consecutive vertices. The area of each such triangle is
[tex]A_{triangle}=\dfrac{1}{2}a^2\sin \alpha=\dfrac{1}{2}\cdot 12^2\cdot \sin60^{\circ}=\dfrac{1}{2}\cdot 144\cdot \dfrac{\sqrt{3}}{2}=36\sqrt{3}\ cm^2.[/tex]
Therefore, the area of hexagon is
[tex]A_{hexagon}=6A_{triangle}=6\cdot 36\sqrt{3}=216\sqrt{3}\approx 374.12\ cm^2[/tex]
