Imagine you have any number of equilateral triangles all of the same size as well as a large number of $30$ $^\circ$ , $30$ $^\circ$ , $120$ $^\circ$ isosceles triangles with the shorter sides the same length as the equilateral triangles.

Using these triangles how many differently shaped rectangles can you build?

Can you make a square?

The interactivity below may help you with this problem. Click on the green or yellow triangles to get a copy. Drag the triangle by its interior to the required position and drag any vertex to rotate it.

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