Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Can you explain why it is impossible to construct this triangle?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?