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?
The figure shows a regular hexagon formed by 6 congruent equilateral triangles that meet at the center point. A side of the hexagon is 7 centimeters.
(1 point)
Responses
21 cm²
21 cm²
73.5Start Root 3 End Rootcm²
73.5 Image with alt text: Start Root 3 End Root cm²
98Start Root 3 End Rootcm²
98 Image with alt text: Start Root 3 End Root cm²
1,029 cm²
1,029 cm²
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To find the area of each hexagonal shape, we need to find the area of one equilateral triangle and then multiply it by 6.
The formula for the area of an equilateral triangle is: (sqrt(3) / 4) * s^2, where s is the length of a side.
In this case, the length of a side is 7 centimeters.
Plugging this value into the formula, we get:
Area of one equilateral triangle = (sqrt(3) / 4) * 7^2
= (sqrt(3) / 4) * 49
= 49sqrt(3) / 4
Finally, to get the area of the hexagonal shape, we simply multiply the area of one equilateral triangle by 6:
Area of each hexagonal shape = 6 * (49sqrt(3) / 4)
= 294sqrt(3) / 4
= 73.5sqrt(3) cm²
So, the exact area of each hexagonal shape is 73.5sqrt(3) cm².