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8. 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

Respuesta :

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

[tex] Area=\frac{1}{2} *a*b*sin C [/tex]

in this problem

a=b=7 cm

C=60 degrees

so

[tex] Area=\frac{1}{2} *7*7*sin 60 [/tex]

[tex] Area=\frac{1}{2} *49*\frac{\sqrt{3}}{2} \\ Area=49*\frac{\sqrt{3}}{4} [/tex]cm²

Step 2

To calculate the area of the hexagon multiply the area of one equilateral triangle by [tex] 6 [/tex]

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

therefore

the answer is the option

73.5 sqrt 3cm²

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