Perimeter of Polygon- Formula, Definition, Examples

The perimeter of a polygon is the total distance around its outer boundary, found by adding the lengths of all its sides. Polygons are flat shapes with straight sides and can be regular (all sides equal) or irregular (different side lengths). Shapes can also be convex or concave, but the method of finding the perimeter remains the same. This concept is widely used in geometry and everyday measurements.

Nivedita Dar22 Jan, 2026

The perimeter of polygon represents the total distance around its outer boundary. You find this value by adding the lengths of every side together. Whether the shape is regular, with equal sides, or irregular, with different side lengths, the concept remains the same. Measuring this path is a fundamental skill used in geometry and real-world construction projects.

Perimeter of Polygon

Let’s talk about what this idea means in real life. A polygon is just a flat shape with straight sides. The word comes from "poly" (meaning many) and "gonia" (meaning angle). Think of the perimeter as a fence around a park. If you walk all the way around the edge of a shape until you get back to the start, that total distance is the perimeter. This measurement is often summarized by the perimeter of polygons definition, which simply states it is the sum of all exterior side lengths.

In school, we put these shapes into two groups. A regular polygon has sides that are all the same length. They have equal sides and equal corners. An irregular polygon is different because its sides are not all the same. We also have Convex shapes where the corners poke out, and Concave shapes where at least one part "caves" in. No matter the shape, the perimeter is just the total length of the outside edge.

Perimeter of Polygon Formula

You don't need to be a math expert to learn the perimeter of polygon formula. Since the perimeter is just the total length of the edge, the main rule is to add up every side. But, we can use quick tricks for some shapes.

Regular Polygons

For regular shapes, the math is very fast. Since every side is the same, you just multiply the length of one side by how many sides there are.

Formula: P = n \times s
n = Number of sides
s = Length of one side

For example, if you have a regular hexagon (6 sides) and each side is 5 cm, the math is 6 \times 5 = 30 cm. This trick saves a lot of time!

Irregular Polygons

When the sides are all different, we go back to the basic way. You must add each side one by one.

Formula: P = s_1 + s_2 + s_3 + ... + s_n
s = The length of each side

Common Shape Formulas

Shape	Sides	Specific Formula
Equilateral Triangle	3	3 \times s
Isosceles Triangle	3	a + a + b (two sides are the same)
Rectangle	4	2 \times (length + width)
Square	4	4 \times s
Parallelogram	4	2 \times (a + b)
Pentagon	5	5 \times s (if regular)
Hexagon	6	6 \times s (if regular)

Using a Perimeter of Polygon Calculator

In class, you might use a perimeter of polygon calculator to check your answers. These tools are great for shapes with many sides. You just type in the number of sides and how long they are, and the computer does the adding for you. Many tools will show you exactly how they added the numbers.

Calculators are helpful, but you should learn how to do it by hand first. Knowing how the math works helps you see if you made a mistake. A calculator is like a helper, but your brain is the boss. When you use these tools, always check if the units (like inches or cm) are the same. If you mix different units, the answer will be wrong.

Finding Perimeter on a Grid

Sometimes you don't know the side lengths, but the shape is on a piece of graph paper. To find the perimeter:

Count the number of units along each straight edge.
If the lines are slanted, use a ruler to measure them.
Add all those numbers together.

Perimeter of Polygons Worksheet

The best way to get good at math is to keep trying. Teachers use a perimeter of polygons worksheet to help you see these shapes clearly. These papers usually have many different shapes. You might see a star or a big "L" shape.

Doing a worksheet helps you see that it doesn't matter if a shape is turned sideways—the perimeter stays the same. Start with shapes that have easy numbers like 2, 5, or 10. Later, try to find a missing side if the teacher tells you the total perimeter. This makes you a better problem solver.

Perimeter of Polygon Examples

Let's look at some perimeter of polygons examples you might find in your homework. We will do them step-by-step.

Example 1: The Regular Octagon

A stop sign has 8 sides that are all the same. If one side is 10 inches long, what is the perimeter?

Step 1: Count the sides (8).
Step 2: Look at the length (10).
Step 3: Multiply them (8 \times 10).
Result: The perimeter is 80 inches.

Example 2: The Irregular Shape

Imagine a shape with four sides. The sides are 5 cm, 7 cm, 10 cm, and 4 cm.

Step 1: Put all the numbers in a list.
Step 2: Add them up: 5 + 7 + 10 + 4.
Step 3: 5 + 7 = 12; 12 + 10 = 22; 22 + 4 = 26.
Result: The perimeter is 26 cm.

Example 3: Perimeter of a Rectangle

A garden has a length of 12 meters and a width of 10 meters.

Step 1: Use the rule 2 \times (length + width).
Step 2: 12 + 10 = 22.
Step 3: 2 \times 22 = 44.
Result: The perimeter is 44 meters.

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