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 9 centimeters, what will be the exact area of each hexagonal shape?
each hexagon will consist of six triangles.
Recall that the area of an equilateral triangle of side s is
A = √3/4 s^2
so each hexagon will have area 3√3*9^2 = 243√3
do mine first ik the answer to yours
or, use the fact that the area of the hexagon is apothem * perimeter:
9√3/2 * 6*9 = 243√3
To find the exact area of each hexagonal shape, we need to know the formula for the area of a hexagon.
The area of a regular hexagon can be calculated using the formula:
Area = (3√3 * s²) / 2
Where 's' represents the length of each side of the hexagon.
In this case, the length of each side of the equilateral triangle (which is also the side length of the hexagon) is given as 9 centimeters.
Plugging in the value of 's' into the formula, we get:
Area = (3√3 * 9²) / 2
Area = (3√3 * 81) / 2
Next, we can simplify this expression:
Area = (243√3) / 2
So, the exact area of each hexagonal shape formed by the blue tiles is (243√3) / 2 square centimeters.