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  1. 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 7 centimeters, what will be the exact area of each hexagonal shape?

(1 point)

21 cm²

73.5 sqrt 3cm²

98 sqrt 3 cm²

1,029 cm²

Verified Answer :

meerkat18

Find the area of the triangle and multiply it by 6 to find the area of the hexagon. So the correct answer is 73.5 sqrt 3cm². Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

calculista

Step 1

Find the area of one equilateral triangle

Applying the law of sines

\(Area=\frac{1}{2} *a*b*sin C\)

in this problem

a=b=7 cm

C=60 degrees

so

\(Area=\frac{1}{2} *7*7*sin 60\)

\(Area=\frac{1}{2} *49*\frac{\sqrt{3}}{2} \\ Area=49*\frac{\sqrt{3}}{4}\)cm²

Step 2

To calculate the area of the hexagon multiply the area of one equilateral triangle by \(6\)

\(Area Hexagon=6*[49*\frac{\sqrt{3}}{4}] \\ Area Hexagon=73.5*\sqrt{3}\)cm²

therefore

the answer is the option

73.5 sqrt 3cm²

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