Given the information on the picture, we can find the apothem of the hexagon using the following formula:
[tex]a=\sqrt[]{\frac{3}{4}s^2}[/tex]
in this case, we have the following:
[tex]\begin{gathered} a=\sqrt[]{\frac{3}{4}(12)^2}=\sqrt[]{108}=10.4 \\ \Rightarrow a=10.4 \end{gathered}[/tex]
now that we have that the apothem is a = 10.4, we can find easily the perimeter by multiplying by 6 the measure of the side:
[tex]P=6(12)=72\operatorname{cm}[/tex]
finally, now that we have the perimeter is P = 72 cm and the apothem, we can find the area of the hexagon:
[tex]\begin{gathered} A=\frac{P\cdot a}{2} \\ \Rightarrow A=\frac{72(10.4)}{2}=374.4\operatorname{cm}^2 \end{gathered}[/tex]
therefore, the area of the hexagon is 374.4cm^2
