The perimeter is the total distance around the shape.
To find the length of each side, divide the perimeter by the number of sides.
This works because all sides of a regular polygon are the same.
✏️ Worked Examples — Finding the Length of Each Side
Example 1 — Regular Pentagon
The perimeter of a regular pentagon is 45 inches. What is the length of each side?
A regular pentagon has 5 equal sides. Since all sides have the same length, divide the perimeter by 5.
\(P=45\text{ in}\)
\(\displaystyle s=\frac{P}{5}\)
\(\displaystyle s=\frac{45}{5}\)
Divide to find the length of one side.
\(s=9\)
\(\boxed{s=9\text{ in}}\)
Example 2 — Regular Heptagon
The perimeter of a regular heptagon is 56 inches. What is the length of each side?
A regular heptagon has 7 equal sides. Since all sides have the same length, divide the perimeter by 7.
\(P=56\text{ in}\)
\(\displaystyle s=\frac{P}{7}\)
\(\displaystyle s=\frac{56}{7}\)
Divide to find the length of one side.
\(s=8\)
\(\boxed{s=8\text{ in}}\)
Example 3 — Regular Octagon
The perimeter of a regular octagon is 72 inches. What is the length of each side?
A regular octagon has 8 equal sides. Since all sides have the same length, divide the perimeter by 8.
\(P=72\text{ in}\)
\(\displaystyle s=\frac{P}{8}\)
\(\displaystyle s=\frac{72}{8}\)
Divide to find the length of one side.
\(s=9\)
\(\boxed{s=9\text{ in}}\)
🧠 Math Vocabulary
Perimeter: The total distance around a figure.
Polygon: A closed figure made of straight line segments.
Regular polygon: A polygon with all sides equal.
Side length: The length of one edge of the polygon.
💡 Main Idea
To find the length of each side of a regular polygon, divide the total perimeter by the number of sides. This works because every side has the same length.
📚 What You Should Already Know
Students should understand how to divide whole numbers and know that perimeter means adding all side lengths.
🚀 What Comes Next
Next, students will apply perimeter concepts to irregular polygons, word problems, and real-world situations involving distance around shapes.
