The figure is made of identical triangles.
- Complete the table for layers 9 and 16.
- If each small triangle has a height of 4 cm and a perpendicular base of 3 cm, find the area of all the triangles at the 29th layer.
Layer number |
Number of triangles |
1 |
1 |
2 |
3 |
3 |
5 |
4 |
7 |
... |
... |
9 |
(i) |
... |
... |
16 |
(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 16
= 16 + (16 - 1)
= 16 + 15
= 31
(b)
Number of triangles in the 29th layer
= 29 + (29 - 1)
= 29 + 28
= 57
Area of one small triangle
=
12 x 4 x 3
= 6 cm
2Area of all the triangles at the 29th layer
= 6 x 57
= 342 cm
2 Answer(s): (a) 17, 31; (b) 342 cm
2