Grid triangles
This task is about continuing a pattern of triangles, and finding a rule.
a) 
On the grid of squares above, draw the next 2 shapes in this series of triangles.


b) 
Complete this table, giving the area of each triangle:


c)

How many squares will be in a triangle of height ...


i) ii) 
10 squares? __________ squares 20 squares? __________ squares 

d)

Explain or write a rule that describes how to work out the total number of squares (area) needed for any given height of triangle.


e)

Show how to work out the height of a triangle that has 81 squares in it.
