Perimeter of Polygons
Learn how to calculate the distance around any polygon by adding up all its sides.
Definition
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Worked Examples
A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?
Identify the sides
Length = 8 cm, Width = 5 cm → Two sides of 8 cm, two sides of 5 cm
Add all sides
→ cm
Or use the formula
→ cm
Answer: The perimeter is 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 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
Triangle Explorer
Area:
20000.0 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 problemsWhat is the perimeter of a rectangle with length 6 cm and width 4 cm?
Why It Matters
- 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?
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 m of fencing.
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 cm of wood.
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 m.
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:
- 3Rectangle: or
- 4Regular polygon: (number of sides times side length)
- 5Always include units in your answer
Frequently Asked Questions
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