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 below. If the side of each tile measures 10 cm, what will be the height of each hexagonal shape?
From the figure above, the height of the hexagon is twice the height of one equilateral triangle.
As for the height of the equilateral triangle, you can subdivide the bottom triangle into two right triangles, with sides 5cm, 10 cm and h=height of triangle.
h can be calculated using Pythagoras theorem:
h²=√(5²+10²)
The height of the hexagon is therefore 2h.
To find the height of the hexagonal shape, we can use the formula for the height of an equilateral triangle.
In an equilateral triangle, the height is equal to the side length multiplied by the square root of 3 divided by 2.
Given that the side length of each tile is 10 cm, we can calculate the height of the hexagonal shape as follows:
Height = Side length * √3 / 2
Height = 10 cm * (√3 / 2)
Height = 10 cm * 1.732 / 2
Height ≈ 8.66 cm
Therefore, the height of each hexagonal shape in the ceramic tile design will be approximately 8.66 cm.
To determine the height of each hexagonal shape, you need to understand the properties of equilateral triangles and hexagons.
1. The height of an equilateral triangle is the distance from any vertex (top point) to the midpoint of the opposite side.
2. The hexagon can be divided into six equilateral triangles, where each triangle is formed by connecting the midpoints of two consecutive sides of the hexagon.
Now, let's break down the problem step by step:
Step 1: Determine the height of one of the equilateral triangles:
Since each side of the equilateral triangle measures 10 cm, the height of the triangle can be found using the formula for the height of an equilateral triangle: h = (√3 / 2) * s, where s represents the length of one side.
In this case, s = 10 cm.
Plugging the value into the formula:
h = (√3 / 2) * 10 cm
h = (√3 / 2) * 10 cm
h = (√3 / 2) * 10 cm
h ≈ 8.66 cm
Step 2: Determine the height of the hexagon:
Since the hexagon is composed of six equilateral triangles, the height of the hexagon will be equal to the height of one of the equilateral triangles.
Therefore, the height of the hexagon will also be 8.66 cm.
So, the height of each hexagonal shape in your bathroom will be approximately 8.66 cm.