You are planning to use a ceramic tile design in your new bathroom the tiles are blue and white

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 317 People

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

Answered by maham237 @ 02/12/2020

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

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

$Area=\frac{1}{2} *49*\frac{\sqrt{3}}{2} \\ Area=49*\frac{\sqrt{3}}{4}$ 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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