By beginning with triangles the children use a familiar shape and can discuss the properties of different types of triangles. If this page is printed, if would be practical to make several copies available to the children who can colour in different shapes to keep track of their findings. This will help as they look for other polygons. Although trial and error is one way to solve this problem of dividing the larger space, some visualising and planning before tackling the problem will lead to a more considered solution. The first consideration is how many lines does it take to divide regions.
Youngsters often think that it requires four lines to divide the rectangle in to four regions.
This also leads to a discussion of the difference between dividing in half as opposed to two, dividing into quarters as opposed to four sections. The stipulation that one of each of the shapes has to be in each section provides a way to review the properties of the different polygons.