A rectangle has 6 seats around it (Figure 1). When arranged together, the rectangle has the following number of seats around it.
- How many seats are there if 4 rectangles are joined together?
- How many seats are there if 31 rectangles are joined together?
- Which figure has 290 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 4 rectangles
= 4 x 4 + 2
= 18
(b)
Number of seats for 31 rectangles
= 31 x 4 + 2
= 126
(c)
Number of seats = Figure number x 4 + 2
Figure number = (Number of seats - 2) ÷ 4
Figure number
= (290 - 2) ÷ 4
= 288 ÷ 4
= 72
Answer(s): (a) 18; (b) 126; (c) 72