Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Pin those squares down! A geoboard is a piece of wood with pins
hammered into it. The diagram shows a 5 by 5 board with 25 pins set
out in a square array. Squares are made by stretching rubber bands
round specific pins as shown. What is the total number of squares
that can be made on a 5 by 5 board? How many squares can be made on
an N by N board?