Question

the relationship between the perimeter and side length of a regular hexagon is shown in the graph below
what happens to the perimeter of a regular hexagon as its side length increases by 1?

• the perimeter increases by 6.
• the perimeter increases by 1.
• the perimeter increases by 3.
• the perimeter increases by 12.

Explanation:

Step1: Recall the formula for the perimeter of a regular hexagon

A regular hexagon has 6 equal sides. So the perimeter \( P \) of a regular hexagon with side length \( s \) is given by the formula \( P = 6s \).

Step2: Analyze the change in perimeter when side length increases by 1

Let the original side length be \( s \), so the original perimeter is \( P_1=6s \).
If the side length increases by 1, the new side length is \( s + 1 \), and the new perimeter is \( P_2=6(s + 1)=6s+6 \).
To find the change in perimeter, we calculate \( P_2 - P_1=(6s + 6)-6s = 6 \).
We can also verify this from the graph. For example, when \( s = 1 \), the perimeter (from the graph) should be \( 6\times1 = 6 \), when \( s = 2 \), the perimeter should be \( 6\times2=12 \), the difference between \( s = 2 \) and \( s = 1 \) is \( 12 - 6 = 6 \). Similarly, for \( s = 3 \), perimeter is \( 18 \), difference from \( s = 2 \) is \( 18 - 12 = 6 \). So the perimeter increases by 6 when the side length increases by 1.

Answer:

The perimeter increases by 6. (Corresponding to the option "The perimeter increases by 6")