Question

What is the rule to represent the number of tiles in figure x?

Answer 1

Figure 1 has 8 tiles
figure 2 has 14 tiles
figure 3 has 22 tiles

I'm guessing the 2 on the side hints for us to do something+2
the inside parts are
figure 1: 6
figure 2: 12
figure 3: 20

hmm, the width is 1+number figure
height is 2+figure number

so therefor, figure x is (1+x)(2+x)+2

so the rule is figure x has (x+1)(x+2)+2 or $x^2+3x+4$ tiles



a. the rule is figure x has (x+1)(x+2)+2 or $x^2+3x+4$ tiles
b. it is quadratic because it has $x^2$ in it