Perimeter of Polygons

Learn how to calculate the distance around any polygon by adding up all its sides.

Elementary20 minLesson
Printable worksheet

Definition

The perimeter of a polygon is the total distance around the outside of the shape. To find the perimeter, add the lengths of all the sides.
Perimeter=Side1+Side2+Side3+⋯\text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Side}_3 + \cdots
For a rectangle with length ll and width ww:
P=2l+2w=2(l+w)P = 2l + 2w = 2(l + w)
For a regular polygon with nn equal sides of length ss:
P=n×sP = n \times s

Try it now

What is the perimeter of a rectangle with length 6 cm and width 4 cm?

Worked Examples

A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?
1

Identify the sides

Length = 8 cm, Width = 5 cm → Two sides of 8 cm, two sides of 5 cm
2

Add all sides

P=8+5+8+5P = 8 + 5 + 8 + 5 → P=26P = 26 cm
3

Or use the formula

P=2(l+w)=2(8+5)=2(13)P = 2(l + w) = 2(8 + 5) = 2(13) → P=26P = 26 cm

Common Mistakes

Only adding two sides of a rectangle

Why it's wrong: A rectangle has four sides, not two. Students sometimes add just length + width instead of all four sides.

Correct: Remember: a rectangle has 2 lengths AND 2 widths. Use P=2l+2wP = 2l + 2w or add all four sides.

Confusing perimeter with area

Why it's wrong: Area measures the space inside; perimeter measures the distance around.

Correct: Perimeter is like walking around the edge. Area is like covering the floor with tiles.

Forgetting units in the answer

Why it's wrong: Perimeter is a length measurement and needs units (cm, m, ft, etc.).

Correct: Always include units! If sides are in meters, the perimeter is in meters.

Interactive Visual

Area and perimeter

l = 8w = 5

Area40

A=l⋅w=8⋅5=40A = l \cdot w = 8 \cdot 5 = 40

Perimeter26

P=2(l+w)=2(8+5)=26P = 2(l + w) = 2(8 + 5) = 26

Diagonal9.43

d=l2+w2=89≈9.43d = \sqrt{l^2 + w^2} = \sqrt{89} \approx 9.43

The two diagonals of a rectangle are always equal.

Triangle Explorer

By sides:Isosceles
By angles:Acute

Area:

20,000.0 sq units

Drag the vertices to change the triangle shape.

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

16 problems
Problem 1 of 16
Easy
What is the perimeter of a rectangle with length 6 cm and width 4 cm?

Why It Matters

Perimeter is used constantly in everyday life:
  • Fencing a yard: How much fence do you need to surround a garden?
  • Picture frames: What length of wood frames a painting?
  • Running tracks: How far is one lap around the track?
  • Wrapping gifts: How much ribbon to wrap around a box?
Anytime you need to measure the distance around something, you're using perimeter!

Real World Applications

Fencing a Garden

Gardeners calculate perimeter to know how much fencing to buy.

Example:

A rectangular garden is 12 m long and 8 m wide. You need P=2(12+8)=40P = 2(12 + 8) = 40 m of fencing.

1Try It Yourself

You want to fence a square garden with sides of 7 m.

How many meters of fencing do you need?

Step 1: Write the mathematical expression

For a square, all 4 sides are equal:

Picture Framing

Frame makers need to know the perimeter to cut the right amount of wood or metal.

Example:

A photo is 20 cm by 25 cm. The frame needs P=2(20+25)=90P = 2(20 + 25) = 90 cm of wood.

2Try It Yourself

An artist has a square painting with sides of 50 cm.

How much frame material is needed?

Step 1: Write the mathematical expression

Calculate the perimeter of the square:

Running Track

Runners need to know the perimeter to track their distance.

Example:

A rectangular field is 100 m by 60 m. One lap is P=2(100+60)=320P = 2(100 + 60) = 320 m.

3Try It Yourself

A park has a triangular walking path with sides of 150 m, 200 m, and 250 m.

How far is one complete lap?

Step 1: Write the mathematical expression

Add all three sides:

Key Takeaways

  • 1Perimeter is the total distance around a polygon
  • 2Add all sides together: P=s1+s2+s3+⋯P = s_1 + s_2 + s_3 + \cdots
  • 3Rectangle: P=2l+2wP = 2l + 2w or P=2(l+w)P = 2(l + w)
  • 4Regular polygon: P=n×sP = n \times s (number of sides times side length)
  • 5Always include units in your answer

Frequently Asked Questions

Perimeter measures the distance around a shape (like a fence). Area measures the space inside a shape (like carpet covering a floor). Perimeter is measured in units (m, cm). Area is measured in square units (m², cm²).
Perimeter measures the distance around a shape (like a fence). Area measures the space inside a shape (like carpet covering a floor). Perimeter is measured in units (m, cm). Area is measured in square units (m², cm²).
Yes! A 1×8 rectangle and a 3×6 rectangle both have perimeter 18, but different areas (8 vs 18 square units).
Yes, but we call it the circumference. It's calculated differently using C=2πrC = 2\pi r or C=πdC = \pi d.

Glossary

Perimeter
The total distance around the outside of a polygon
Polygon
A closed 2D shape with straight sides (triangle, rectangle, hexagon, etc.)
Regular polygon
A polygon where all sides are equal length and all angles are equal
Length
The longer side of a rectangle
Width
The shorter side of a rectangle
Today's challengeOne problem, three tries

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