There is one rectangle in Figure 1
There are 3 rectangles in Figure 2 (two small and the one made of two)
There are 6 rectangles in Figure 3 (three small, two made of two and one made of three)
What figure number corresponds to 28 small congruent rectangles?
To determine the figure number that corresponds to 28 small congruent rectangles, we can analyze the pattern in the number of rectangles for each figure.
In Figure 1, there is only one rectangle.
In Figure 2, there are 3 rectangles (2 small and 1 made of two small rectangles).
In Figure 3, there are 6 rectangles (3 small, 2 made of two, and 1 made of three small rectangles).
We can observe that the number of rectangles in each figure follows a pattern: 1, 3, 6.
The pattern can be described as follows:
- The first figure has 1 rectangle.
- The second figure has the previous figure's count plus 2 (1 + 2 = 3).
- The third figure has the previous figure's count plus 3 (3 + 3 = 6).
We see that the pattern increments by 2 and then 3.
So, to find the figure number that corresponds to 28 small congruent rectangles, we need to determine which number in the pattern 1, 3, 6, 10, 15, ... is equal to or greater than 28.
Using the pattern, we can calculate the next few numbers:
1, 3, 6, 10, 15, 21, 28, ...
The pattern continues with the next number being 36.
Therefore, the figure number corresponding to 28 small congruent rectangles is Figure 7.