now, the blue tiles are just equilateral triangles, you grab 6 of them, and slap them around like a hexagon, we know each side is 4, if we sit one on the ground the base of one is just 4 then, what is its height or altitude anyway?
[tex]\bf \textit{height of an equilateral triangle}\\\\
h=\cfrac{s\sqrt{3}}{2}~~
\begin{cases}
s=length~of\\
\qquad a~side\\
-------\\
s=4
\end{cases}\implies h=\cfrac{4\sqrt{3}}{2}\implies h=2\sqrt{3}\\\\
-------------------------------\\\\
\textit{area of one of those equilateral blue tiles}\\\\
A=\cfrac{1}{2}~~\stackrel{base}{(4)}~~\stackrel{height}{(2\sqrt{3})}\implies A=4\sqrt{3}
\\\\\\
\stackrel{\textit{area for all 6 blue tiles}}{6(4\sqrt{3})}\implies 24\sqrt{3}[/tex]
