## You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrang

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

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c

m

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2022-04-14T16:48:02+00:00
2022-04-14T16:48:02+00:00 1 Answer
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## Answers ( 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 groundthe base of one is just 4 then, what is its height or altitude anyway?

[tex]bf textit{height of an equilateral triangle}nh=cfrac{ssqrt{3}}{2}~~nbegin{cases}ns=length~ofnqquad a~siden——-ns=4nend{cases}implies h=cfrac{4sqrt{3}}{2}implies h=2sqrt{3}n——————————-ntextit{area of one of those equilateral blue tiles}nA=cfrac{1}{2}~~stackrel{base}{(4)}~~stackrel{height}{(2sqrt{3})}implies A=4sqrt{3}nnstackrel{textit{area for all 6 blue tiles}}{6(4sqrt{3})}implies 24sqrt{3}[/tex]