Well done to Book and Priya from Bangkok Patana School in Thailand, who sent us their work on this problem:

When moving around some of the smaller shapes cut out from the equilateral triangle, we actually found many solutions for making trapezia using trial and error, but also remembered to include irregular trapezia. In total, we made 15 trapezia!

To start off, you should write down all the angles in the small shapes, since it makes it easier to calculate the angles to check if you actually made a trapezium. Look in the equilateral triangle diagram and see if you can spot any possible trapezia from just looking. After that, try adding more triangles to it to make new ones but be sure to check if the total of the interior angles adds up to $360^\circ$.

Book and Priya were able to find the angles in each of the cut out shapes and they were able to make 15 different trapezia.

- If the area of the smallest equilateral triangle is one unit, what is the area of each of the other shapes?
- How many different parallelograms (which are not rectangles) can you make?
- How many different rectangles can you make?
- Which other quadrilaterals can you make?