Understanding how to calculate the length of each side of a polygon when given the perimeter is an essential skill in geometry. This guide will show you step-by-step how to find the side length of a regular 5-sided polygon (pentagon) given the perimeter.
Step 1: Show the Perimeter Formula
The formula for the perimeter \(P\) of a regular polygon with \(n\) sides, each of length \(s\), is:
\[ P = n \cdot s \]
Step 2: Explain the Formula
In this formula:
- \(P\) represents the perimeter of the polygon.
- \(n\) is the number of sides in the polygon.
- \(s\) is the length of each side.
To find the length of each side \(s\), we can rearrange the formula:
\[ s = \frac{P}{n} \]
Step 3: Insert Numbers as an Example
Let's say we have a regular pentagon (a polygon with 5 equal sides) and the perimeter \(P\) is 40 units. We can calculate the side length using the formula:
\[ s = \frac{P}{n} \]
Given:
- \(P = 40\) units
- \(n = 5\)
Step 4: Calculate the Final Value
Substitute the values into the formula:
\[ s = \frac{40}{5} \]
\[ s = 8 \]
So, the length of each side of the pentagon is 8 units.
Final Value
The length of each side of a regular 5-sided polygon (pentagon) with a perimeter of 40 units is 8 units.
