The equilateral triangles are formed using 3-cm sticks.
- How many sticks are needed to form Pattern 8?
- In which pattern will each side of the triangle measure 57 cm?
- Calculate the number of shaded triangles in Pattern 100.
(a)
Number of sticks:
Pattern
1: 1 x 3 = (
1) x
3 = 3 sticks
Pattern
2: 3 x 3 = (1 +
2) x
3 = 9 sticks
Pattern
3: 6 x 3 = (1 + 2 +
3) x
3 = 18 sticks
Pattern
4: 10 x 3 = (1 + 2 + 3 +
4) x
3 = 30 sticks
Sum of numbers = Pattern Number x (Pattern Number + 1) ÷ 2
Formula:
Number of sticks = Sum of numbers up to Pattern Number x 3
Number of sticks needed for Pattern 8
= (1 + 2 + 3 + ... + 8) x 3
= [8 x (8 + 1) ÷ 2] x 3
= [8 x 9 ÷ 2] x 3
= 36 x 3
= 108
(b)
Length of each side of the triangle:
Pattern
1: 1 x
3 = 3 cm
Pattern
2: 2 x
3 = 6 cm
Pattern
3: 3 x
3 = 9 cm
Pattern
4: 4 x
3 = 12 cm
Formula:
Length of each side of the triangle = Pattern Number x
3Pattern Number with each side of the triangle measuring 57 cm
= 57 ÷ 3
= 19
(c)
Pattern
1: Number of shaded triangles =
0 Pattern
2: Number of shaded triangles = 0 +
1 Pattern
3: Number of shaded triangles = 0 + 1 +
2 Pattern
4: Number of shaded triangles = 0 + 1 + 2 +
3 Pattern for number of shaded triangles = Sum of numbers up to (
Pattern Number - 1)
Number of shaded triangles in Pattern 100
= [(Pattern Number - 1) x (Pattern Number)] ÷ 3
= (99 x 100) ÷ 3
= 3300
Answer(s): (a) 108; (b) 19; (c) 3300
