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String Lights & Perimeter

QUICK LINKS


String Lights & Perimeter

Perimeter of Polygons

Perimeter is the total distance around the border of a 2D shape. To find the perimeter of a polygon, we need to find the length of each of its sides, then add them all together.

To help us visualize this process, let's imagine we want to brighten up a room by lining it with some string lights.
The perimeter is like the total length of string lights we need to line the walls.
If each of our walls has length , then we need a total string light length of to line the room.
So the perimeter of this room is also equal to . Perimeters are lit ✨.
Check out our calculator or continue the lesson to explore finding the perimeter of different shapes!

Perimeter of Polygons Calculator

Step 1. Determine whether the polygon is regular.

The shape is regular if all the sides are the same length.

Step 2. Count the number of sides.

Step 3. Determine the length of one side of the polygon.

The shape is regular, so we only need to know the length of one side to calculate the perimeter.
In the diagram, we can see that one side has length .

Step 4. Add up the side lengths.

The shape is regular, so just multiply the length of one side by the number of sides.
This covers all our sides:
So the perimeter of this shape is .

Key Steps 🗝 How to Find the Perimeter of Polygons

Step 1. Determine whether the polygon is regular.

The shape is regular if all the sides are the same length.

Step 2. Count the number of sides.

Step 3. Determine the lengths of each side of the polygon.

If the shape is regular, all the sides have the same length, so you only need to know the length of one side to calculate the perimeter.
If the shape is not regular, make sure you find the length of every side you counted in Step 2.

Step 4. Add up the side lengths.

If the shape is regular, just multiply the length of one side by the number of sides.
If the shape is not regular, add up all the side lengths you found in Step 3.
Walk through some perimeter example problems and try some practice problems on your own!

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Perimeter of Polygons

Finding the perimeter of a polygon is like finding the total length of string lights needed to line a room.
If we have a regular polygon, meaning the sides are all the same length, we only need to find the length of one side and then multiply it by the number of sides:
If the shape is not regular, we have to find the length of every side and then add them all up together. The number of side lengths we add up should match the number of sides.
Let’s walk through some perimeter example problems together!
Let's start here. Find the perimeter of this regular polygon:

Step 1. Determine whether the polygon is regular.

The shape is regular if all the sides are the same length. We are told this shape is regular, so we know the sides are the same.

Step 2. Count the number of sides.

This shape has sides.

Step 3. Determine the length of one side of the polygon.

The shape is regular, so we only need to know the length of one side to calculate the perimeter.
In the diagram, we can see that one side has length .

Step 4. Add up the side lengths.

The shape is regular, so just multiply the length of one side by the number of sides.
This covers all our sides:
So the perimeter of this shape is .
Nice work! Now let's try an irregular polygon 😮. Find the perimeter of this polygon:

Step 1. Determine whether the polygon is regular.

The shape is regular if all the sides are the same length. The sides have different lengths, so this shape is not regular.

Step 2. Count the number of sides.

This shape has sides.

Step 3. Determine the lengths of the 4 sides of the polygon.

From the diagram, we can see that our shape has side lengths .

Step 4. Add up the side lengths.

Add up all the side lengths from Step 3. Make sure we've covered every side of the shape:
This might not look exactly like your shape, but just remember to light up and include every side length for the perimeter! 💡
So the perimeter of this shape is .

What if there's a missing side length?

When we're missing a side length of a polygon, we can use a parallel side length to find the missing value:
If you’d like additional practice with finding the perimeter of polygons, take a moment to complete the quick practice below before closing out this lesson! ⚡

Practice: Perimeter of Polygons

Question 1 of 8: Find the perimeter of this regular polygon:

Step 1. Determine whether the polygon is regular.

The shape is regular if all the sides are the same length. What is this shape?

Step 2. Count the number of sides of the polygon.

Step 3. Determine the length of one side of the polygon.

If the shape is regular, all the sides have the same length, so you only need to know the length of one side to calculate the perimeter.

Step 4. Add up the side lengths.

The shape is regular, so just multiply the length of one side by the number of sides.
Great work! The perimeter of this polygon is  .

When you feel like you've mastered this lesson, click for a celebration ⬇️!
Incredible job, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?