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 10?
- If there is a total of 117 triangles, how many layers are there in the figure?
(a)
Pattern of the total number of triangles
Layer 1 = 1 (1 + 2) =
1 x
3 = 3
Layer 2 = 2 x (1 + 2) =
2 x
3 = 6
Layer 3 = 3 x (1 + 2) =
3 x
3 = 9
Formula:
Total number of triangles =
Layer Number x
3 Total number of triangles if it is drawn up to Layer 10
=
10 x
3 = 30
(b)
Number of layers if there is a total of 117 triangles
= 117 ÷
3 = 39
Answer(s): (a) 30; (b) 39