Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
Can you work out the area of the inner square and give an
explanation of how you did it?
All these triangles have a base of 1 unit and a height of 2 units. We
could call them a "family" of triangles.
What are their areas? What do you notice?
Can you generalise to other "families" of triangles?
You may like to use the interactivity below to investigate more