When working on an isometric grid, we can measure areas in terms of equilateral triangles instead of squares.

Here are some equilateral triangles.

If the area of the first triangle is 1, what are the areas of the other triangles?

Will the pattern continue?

Can you explain why?

All the triangles in the first image had horizontal bases, but it is also possible to draw tilted equilateral triangles.

Here are some equilateral triangles with a tilt of 1.

Can you find a rule to work out the area of any equilateral triangle with a tilt of 1?

Can you explain why your rule works?

What about triangles with a tilt of 2?

What about other tilts?