You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 4 centimeters, what will be the exact area of each hexagonal shape? Question 17 options:12 cm2192 cm224cm2323√cm
Accepted Solution
A:
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]