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

Question 17 options:

12 cm2

192 cm2

24cm2

32
3

√
c
m

Answer 1

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?


`\bf \textit{height of an equilateral triangle}\\\\ h=\cfrac{s√(3)}{2}~~ \begin{cases} s=length~of\\ \qquad a~side\\ -------\\ s=4 \end{cases}\implies h=\cfrac{4√(3)}{2}\implies h=2√(3)\\\\ -------------------------------\\\\ \textit{area of one of those equilateral blue tiles}\\\\ A=\cfrac{1}{2}~~\stackrel{base}{(4)}~~\stackrel{height}{(2√(3))}\implies A=4√(3) \\\\\\ \stackrel{\textit{area for all 6 blue tiles}}{6(4√(3))}\implies 24√(3)`