MATH SOLVE

4 months ago

Q:
# 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]

[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]