Look at the picture.
The area of the hexagon is equal six times the area of the equilateral triangle.
The formula of the equilateral triangle with the leg a:
[tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
Therefore the formula of the area of the hexagon with a side lenght a is:
[tex]A=6\cdot\dfrac{a^2\sqrt3}{4}=\dfrac{3a^2\sqrt3}{2}[/tex]
We have a = 12cm. Substitute:
[tex]A=\dfrac{3\cdot12^2\sqrt3}{2}=\dfrac{3\cdot144\sqrt3}{2}=3\cdot72\sqrt3=216\sqrt3\ cm^2[/tex]
