The figure is made of identical triangles.
- Complete the table for layers 6 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 33rd layer.
Layer number |
Number of triangles |
1 |
1 |
2 |
3 |
3 |
5 |
4 |
7 |
... |
... |
6 |
(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 6
= 6 + (6 - 1)
= 6 + 5
= 11
Number of triangles for layer 16
= 16 + (16 - 1)
= 16 + 15
= 31
(b)
Number of triangles in the 33rd layer
= 33 + (33 - 1)
= 33 + 32
= 65
Area of one small triangle
=
12 x 4 x 3
= 6 cm
2Area of all the triangles at the 33rd layer
= 6 x 65
= 390 cm
2 Answer(s): (a) 11, 31; (b) 390 cm
2