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
To find the area of one equilateral triangle, we can use the formula: Area = (s^2 * sqrt(3))/4, where s is the length of one side of the triangle.
Given that each side of the equilateral triangle (blue tile) measures 7 centimeters, we can plug this value into the formula:
Area = (7^2 * sqrt(3))/4
Area = (49 * sqrt(3))/4
Area = 49sqrt(3)/4
Area = 12.25sqrt(3) square centimeters
Since there are 6 equilateral triangles making up the hexagon, we can find the total area of the hexagon by multiplying the area of one equilateral triangle by 6:
Total area = 6 * 12.25sqrt(3)
Total area = 73.5sqrt(3) square centimeters
Therefore, the exact area of each hexagonal shape is 73.5 square centimeters.