Perimeter - Definition, Examples, Quiz, FAQ, Trivia
Learn how to calculate the distance around shapes with easy explanations and practice activities
What is Perimeter?
Perimeter is the total distance around the outside of a shape. Think of it like walking all the way around your backyard fence. If you measured each side and added them all together, you'd get the perimeter!
Perimeter is measured in units of length like centimeters, inches, feet, or meters. We use perimeter in everyday life when we put up fences around gardens, measure the border of a picture frame, or calculate how much ribbon we need to go around a gift box.
The word "perimeter" comes from Greek words meaning "around measure." It's different from area, which measures how much space is inside the shape.
Key Concept
Perimeter = Total distance around a closed shape
How to Find Perimeter
Finding the perimeter of a shape is simple! Just follow these steps:
1. Identify all the sides of the shape
2. Measure the length of each side
3. Add all the side lengths together
Let's practice with an example:
Example: Find the perimeter of a rectangle that is 5 cm long and 3 cm wide.
Step 1: Identify sides → two sides of 5 cm and two sides of 3 cm
Step 2: Add all sides → 5 + 5 + 3 + 3
Step 3: Calculate → 16 cm
So the perimeter is 16 cm. Remember, perimeter is always a measurement of length.
Remember
For any polygon, the perimeter is simply the sum of all its side lengths.
Perimeter Formulas
While you can always find perimeter by adding all sides, some shapes have special formulas that make calculation easier:
Square
P = 4 × side
Rectangle
P = 2 × (length + width)
Triangle
P = a + b + c
Circle
C = 2πr (Circumference)
Perimeter Formula for Regular Polygons
Where n = number of sides, s = length of each side
Formula Tip
For irregular shapes, you still need to add all the side lengths since the sides aren't equal.
Real-World Examples
Perimeter is all around us! Here are some real-world examples:
Example 1: Fencing a Garden
Mrs. Johnson has a rectangular garden that is 8 meters long and 5 meters wide. How much fencing does she need to go around the entire garden?
Solution: Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 meters
Example 2: Picture Frame Border
A square picture frame has sides of 30 cm. What is the perimeter of the frame?
Solution: Perimeter = 4 × side = 4 × 30 = 120 cm
Example 3: Running Track
A circular running track has a radius of 50 meters. What is the distance around the track? (Use π ≈ 3.14)
Solution: Circumference = 2πr = 2 × 3.14 × 50 = 314 meters
Example 4: Irregular Shape
A pentagon has sides measuring 4 cm, 5 cm, 3 cm, 6 cm, and 4 cm. What is its perimeter?
Solution: Perimeter = 4 + 5 + 3 + 6 + 4 = 22 cm
Look around your classroom or home - how many examples of perimeter can you find?
Real-World Tip
When calculating perimeter for real objects, always remember to measure all sides carefully!
Perimeter Practice Quiz
Test your perimeter knowledge with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about perimeter:
Perimeter Trivia
Discover interesting facts about perimeter:
Ancient Measurements
The concept of perimeter dates back to ancient Egypt where surveyors called "rope-stretchers" measured land boundaries using knotted ropes to calculate perimeters for taxation purposes.
Nature's Perimeter
Honeybees build hexagonal honeycombs because this shape gives the most area for storing honey with the least perimeter, saving them precious wax and energy.
Earth's Perimeter
The Earth's circumference (perimeter) at the equator is about 40,075 kilometers. The ancient Greek mathematician Eratosthenes calculated this over 2,200 years ago with remarkable accuracy!
Perimeter Paradox
Some shapes have finite area but infinite perimeter! The Koch snowflake fractal starts with a triangle but as you add smaller triangles infinitely, the perimeter grows without limit while the area remains finite.
