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Kipish [7]
3 years ago
13

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

ecide 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
Mathematics
2 answers:
ira [324]3 years ago
3 0

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

dlinn [17]3 years ago
3 0
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. 
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