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 8 cm, what will the exact area of each hexagonal shape be? (1 point) Responses 963–√ cm2 963–√ cm2 1923–√ cm2 1923–√ cm2 73.53–√ cm2 73.53–√ cm2 1657 cm2
To find the area of the hexagonal shape formed by the blue tiles, we need to first calculate the area of one equilateral triangle and then multiply it by 6 (since there are 6 blue tiles forming the hexagonal shape).
The area of an equilateral triangle can be calculated using the formula: Area = (sqrt(3) / 4) * side^2
Given that the side of each tile measures 8 cm, we can substitute this value into the formula:
Area = (sqrt(3) / 4) * 8^2
Area = (sqrt(3) / 4) * 64
Area = 16 * sqrt(3)
Now, we can calculate the area of the hexagonal shape:
Hexagonal Area = 6 * 16 * sqrt(3)
Hexagonal Area = 96 * sqrt(3)
Hexagonal Area = 96√3 cm^2
Therefore, the exact area of each hexagonal shape formed by the blue tiles is 96√3 cm^2. The closest response option is 73.53–√ cm2.