The figure is made up for triangles drawn up to the Layer 3.
- How many triangles will there be if it is drawn up to Layer 8?
- If there is a total of 126 triangles, how many layers are there in the figure?
(a)
Pattern of the total number of triangles
Layer 1 = 1 (1 + 2 + 3) =
1 x
6 = 6
Layer 2 = 2 x (1 + 2 + 3) =
2 x
6 = 12
Layer 3 = 3 x (1 + 2 + 3) =
3 x
6 = 18
Formula:
Total number of triangles =
Layer Number x
6 Total number of triangles if it is drawn up to Layer 8
=
8 x
6 = 48
(b)
Number of layers if there is a total of 126 triangles
= 126 ÷
6 = 21
Answer(s): (a) 48; (b) 21