Understanding how to calculate the perimeter of a polygon is essential in geometry. This guide will show you step-by-step how to find the perimeter of a regular 5-sided polygon (pentagon) given the side length.
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.
For a regular polygon, all sides are of equal length. Therefore, the perimeter is simply the product of the number of sides and the length of one side.
Step 3: Insert Numbers as an Example
Let's say we have a regular pentagon (a polygon with 5 equal sides) and each side length \(s\) is 6 units. We can calculate the perimeter using the formula:
\[ P = n \cdot s \]
Given:
- \(n = 5\)
- \(s = 6\) units
Step 4: Calculate the Final Value
Substitute the values into the formula:
\[ P = 5 \cdot 6 \]
\[ P = 30 \]
So, the perimeter of the pentagon is 30 units.
Final Value
The perimeter of a regular 5-sided polygon (pentagon) with each side length of 6 units is 30 units.
