Question

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 9 centimeters, what will be the exact area of each hexagonal shape?

Answer 1

well, there are 6 equilateral triangles, each one with sides of measure of 9 cm.

`\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=9 \end{cases}\implies A=\cfrac{9^2√(3)}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{area for all six triangles} }{6\left( \cfrac{9^2√(3)}{4} \right)}\implies \cfrac{243√(3)}{2}`