The figure is made of identical triangles.
- Complete the table for layers 7 and 16.
- If each small triangle has a height of 3 cm and a perpendicular base of 4 cm, find the area of all the triangles at the 24th layer.
Layer number |
Number of triangles |
1 |
1 |
2 |
3 |
3 |
5 |
4 |
7 |
... |
... |
7 |
(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 7
= 7 + (7 - 1)
= 7 + 6
= 13
Number of triangles for layer 16
= 16 + (16 - 1)
= 16 + 15
= 31
(b)
Number of triangles in the 24th layer
= 24 + (24 - 1)
= 24 + 23
= 47
Area of one small triangle
=
12 x 3 x 4
= 6 cm
2Area of all the triangles at the 24th layer
= 6 x 47
= 282 cm
2 Answer(s): (a) 13, 31; (b) 282 cm
2