The patterns show a sequence of shapes. Each shape has a number of small right-angled triangles. A dot is placed at each point where there is a vertex of one or more right-angled triangles. The total number of dots and the number of small right-angled triangles of each figure is shown in a table.
- Find the total number of dots required to form Pattern 8.
- Find the total number of dots required to form Pattern 89.
- Find the number of small right-angled triangles in Pattern 49.
(a)
Pattern for the total number of dots
Pattern 1: (1 + 1)
2 = 4
Pattern 2: (2 + 1)
2 = 9
Pattern 3: (3 + 1)
2 = 16
Formula
Number of dots = (Pattern number + 1)
2 Number of dots for Pattern 8
= (8 + 1)
2 = 81
(b)
Number of dots in Pattern 89
= (89 + 1)
2 = 90
2 = 8100
(c)
Pattern for the number of small right-angled triangles
Pattern 1: 1
2 x 2 = 2
Pattern 2: 2
2 x 2 = 8
Pattern 3: 3
2 x 2 = 18
Formula
Number of small right-angled triangles = Pattern number
2 x 2
Number of small right-angled triangles in Pattern 49
= 49
2 x 2
= 4802
Answer(s):(a) 81; (b) 8100; (c) 4802