A rectangle has 6 seats around it (Figure 1). When arranged together, the rectangle has the following number of seats around it.

1. How many seats are there if 11 rectangles are joined together?
2. How many seats are there if 36 rectangles are joined together?
3. Which figure has 406 seats together?

(a)
Pattern for the number of seats
Figure 1: 1 x 4 + 2 = 6
Figure 2: 2 x 4 + 2 = 10
Figure 3: 3 x 4 + 2 = 14

Pattern for the number of rectangles
Figure 1: 1
Figure 2: 2
Figure 3: 3

Number of rectangles = Figure number

Number of seats = Figure number x 4 + 2

Number of seats for 11 rectangles
= 11 x 4 + 2
= 46

(b)
Number of seats for 36 rectangles
= 36 x 4 + 2
= 146

(c)
Number of seats = Figure number x 4 + 2
Figure number = (Number of seats - 2) ÷ 4

Figure number
= (406 - 2) ÷ 4
= 404 ÷ 4
= 101

Answer(s): (a) 46; (b) 146; (c) 101