Number of squares in Pattern 1 = 0 = 0 x 0
Number of squares in Pattern 2 = 1 = 1 x 1
Number of squares in Pattern 3 = 4 = 2 x 2
Number of squares in Pattern 4 = 9 = 3 x 3

Notice that number of squares in a certain figure is always

=(Pattern number - 1)x(Pattern number - 1)

So for Pattern 8,

Number of squares = (8 - 1) x (8 - 1)
= 7 x 7
= 49

Your (b) should be = 5 x 5 = 25, not 15.


You can see that the small squares form a bigger square.

For Pattern 3 the bigger square is 2 small squares by 2 small squares. So its length is 2 small squares long.


For Pattern 4 the bigger square is 3 small squares by 3 small squares. So its length is 3 small squares long.

So for Pattern 8, it's 7 small squares by 7 small squares. So its length is 7 small squares long.

A square has 4 sides. Notice that for every pattern, each triangle sits on one outermost small square.

So for Pattern 8, there are 7 triangles on each side of the bigger square.

7 small triangles on each side x 4 sides
= 28 small triangles.


The perimeter of each equilateral triangle is the length of two sides of it.

2 x 1 cm = 2 cm

There are 28 equilateral triangles in Pattern 8.

So perimeter = 2 cm x 28 = 56 cm