The figure is made of identical triangles.
- Complete the table for layers 9 and 12.
- If each small triangle has a height of 6 cm and a perpendicular base of 3 cm, find the area of all the triangles at the 30th layer.
| Layer number |
Number of triangles |
| 1 |
1 |
| 2 |
3 |
| 3 |
5 |
| 4 |
7 |
| ... |
... |
| 9 |
(i) |
| ... |
... |
| 12 |
(ii) |
(a)
1st layer: 0 + 1 = 1 triangle
2nd layer: 1 + 2 = 3 triangles
3rd layer: 2 + 3 = 5 triangles
4th layer: 3 + 4 = 7 triangles
Formula:
Number of triangles in a layer = Pattern number + (Pattern number - 1)
Number of triangles for layer 9
= 9 + (9 - 1)
= 9 + 8
= 17
Number of triangles for layer 12
= 12 + (12 - 1)
= 12 + 11
= 23
(b)
Number of triangles in the 30th layer
= 30 + (30 - 1)
= 30 + 29
= 59
Area of one small triangle
=
12 x 6 x 3
= 9 cm
2Area of all the triangles at the 30th layer
= 9 x 59
= 531 cm
2 Answer(s): (a) 17, 23; (b) 531 cm
2 
