Question

the table below shows the relationship between the side lengths of a regular octagon and its perimeter.

side - length, s (inches)	perimeter, p (inches)

| 1 |

2	16
3	24

| 4 |

9	72
12	96

complete the table.
if gabby wants to make a regular octagon with a side - length of 20 inches more area, how much area does she need? justify your reasoning with an explanation of whether perimeter is proportional to side - length.

Explanation:

Step1: Perimeter formula for regular octagon

A regular octagon has 8 equal sides, so perimeter \( P = 8s \), where \( s \) is side length.

Step2: Complete table for s=5

\( P = 8 \times 5 = 40 \)

Step3: Complete table for s=12

\( P = 8 \times 12 = 96 \)

Step4: Check proportionality

Proportional if \( P/s = \text{constant} \). Here, \( P/s = 8 \) (constant), so proportional.

Answer:

Completed table entries: For side length 5, perimeter is 40; for side length 12, perimeter is 96. The perimeter is proportional to the side length because the ratio of perimeter to side length is constant (8).