Figure 1 has 1 red tile and 8 white tiles (9 total) Figure 2 has 4 red tiles and 12 white tiles (16 total) Figure 3 has 9 red tiles and 16 white tiles (25 total) Figure 4 has 16 red tiles and 20 white tiles (36 total)
Things to notice * The pattern counts for the red tiles are perfect squares (1, 4, 9, 16)
* The total number of tiles are also perfect squares (9, 16, 25, 36)
* The number of white tiles can be counted, but its much easier to use the formula W = T - R W = number of white tiles T = total number of tiles R = number of red tiles
* The pattern for the white tile counts is 8,12,16,20 so we basically add on 4 each time. The formula is W(n) = 4n+4. Plug in n = 1 and it leads to W(n) = 8 as expected. Plug in n = 2 and it leads to W = 12 etc.
The input n is the number of the figure which is a natural number. Natural numbers are {1, 2, 3, 4, ...} which are counting numbers. The function is NOT continuous. We can't plug in n = 1.5 for instance. The input does not represent the number of white tiles as that is the output.
If we plugged in n = 6, then we get W(n) = 4n+4 W(6) = 4*6+4 W(6) = 30 so figure 6 will have 30 white tiles (not 10)
Do the same for n = 8 W(n) = 4n+4 W(8) = 4*8+4 W(8) = 36 figure 8 has 36 white tiles
if we made this into a rectangle (pretend you chop off one of the triangles and glue it to the other one to make a long rectangle), the length would be 10+4.5, or 14.5. to find what h is, we can just divide 116 by 14.5. our answer is 8.
