Posted by Ehrine on Monday, March 28, 2011 at 11:10pm.
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?

geometry  MathMate, Tuesday, March 29, 2011 at 11:20am
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.
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