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 1657 cm2 1657 cm squared 963–√ cm2 963–√ cm2 1923–√ cm2 1923–√ cm2 73.53–√ cm2
To find the area of the hexagonal shape made up of blue tiles, you need to first find the area of each equilateral triangle.
The formula for the area of an equilateral triangle is: Area = (s^2 * √3) / 4, where s is the side length of the triangle.
Given that each side of the blue tile measures 8 cm, we can substitute s = 8 cm into the formula:
Area = (8^2 * √3) / 4
Area = (64 * √3) / 4
Area = 16√3 cm^2
Now, the hexagonal shape is made up of 6 equilateral triangles.
Area of hexagonal shape = 6 * 16√3 cm^2
Area of hexagonal shape = 96√3 cm^2
Therefore, the exact area of each hexagonal shape made up of blue tiles is 96√3 cm^2.