check the picture below.
[tex]\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}~~
\begin{cases}
s=length~of\\
\qquad a~side\\
------\\
s=\frac{s}{3}
\end{cases}\implies A=\cfrac{\left( \frac{s}{3} \right)^2\sqrt{3}}{4}
\\\\\\
A=\cfrac{\frac{s^2\sqrt{3}}{3^2}}{4}\implies A=\cfrac{s^2\sqrt{3}}{4\cdot 3^2}\implies A=\cfrac{s^2\sqrt{3}}{36}
\\\\\\
\textit{and since there are 3 triangles shaded with that area}
\\\\\\
\textit{shaded area}\implies 3\left( \cfrac{s^2\sqrt{3}}{36} \right)\implies \cfrac{s^2\sqrt{3}}{12}[/tex]
