In this problem we are going to be thinking about the areas of
equilateral triangles.
The important thing to keep in mind is that, to make life easy
for ourselves, we will measure our areas in terms of
equilateral triangles too.
Here are some equilateral triangles.
If the area of the first triangle is 1, what are the areas of
the others?
Do you see any patterns?
Are you surprised?
Will these patterns continue? Why?
All the triangles you have just been looking at had horizontal
bases, but of course equilateral triangles can be tilted.
Here are some equilateral triangles with a tilt of 1.
Can you explain what I mean by a tilt of 1?
How do I know they are equilateral triangles? Can you convince
yourself that they are?
Can you find their areas? If
you need some help with this why not use the geoboard
environment below and/or use the hints .
