Page 209 - Math Smart - 7

Example 1

Look at the figures below. Find the number of dots, sticks and triangles in
Figure 9.

Figure 1 Figure 2 Figure 3 Figure 4

Figure Number of dots Number of sticks Number of triangles
1 3 3 1
2 6 9 4
3 10 18 9
4 15 30 16

Solution
Understand the problem
The figures are formed using sticks and each figure has a certain number
of dots and triangles.
Two triangles are added to Figure 1 to form Figure 2, three triangles are
added to Figure 2 to form Figure 3, and so on.
We have to find the number of dots, sticks and triangles in Figure 9.

Make a plan
We look for number patterns from the table.
For total number of dots: 3, 6, 10, 15, ...
For total number of sticks: 3, 9, 18, 30, ...
For total number of triangles: 1, 4, 9, 16, ...

Try it out
-^5
We use the number patterns to find the information on Figure 9.
To find the number of dots, we add the next number.
+ 3 +4 +5 +6 +7 +8 +9 +10
^. , ,

The number of dots in Figure 9=15 + 6 + 7 + 8 + 9 + 10
= 55
To find the number of sticks, we add (3 X the next figure number). — 6 = 3X2, 9 = 3X3, 12 = 3X4
+ 6 +9 +12 +15 +18 ^21^^+j^^27^

The number of sticks in Figure 9 = 30 + 15 + 18 + 21 +24 + 27
= 135