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:
 
Height of triangle (number of squares high)
1
2
3
4
Number of squares in the triangle (area)
1
4
 
  
 
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.
 

 
 
 
 

Height = __________ squares