Area and Perimeter - Definition, Examples, Quiz, FAQ, Trivia
Learn how to calculate space inside shapes and the distance around them
What are Area and Perimeter?
Perimeter is the total distance around the outside of a shape. Think of it as the fence around a yard or the outline of a picture frame.
Area is the amount of space inside a shape. Imagine how much paint you'd need to cover a wall or how many tiles would fit on a floor.
These are important concepts in geometry that help us understand the size and space of different objects. Perimeter is measured in linear units (like cm, m, ft), while area is measured in square units (like cm², m², ft²).
Key Concept
Perimeter = Distance around a shape
Area = Space inside a shape
How to Find Area and Perimeter
Finding Perimeter:
To find the perimeter of any polygon, add the lengths of all its sides together. For example, a rectangle with sides 5cm and 3cm has a perimeter of 5 + 5 + 3 + 3 = 16cm.
Finding Area:
For rectangles and squares, multiply the length by the width. For example, a rectangle that is 5cm long and 3cm wide has an area of 5 × 3 = 15cm².
Different shapes have different formulas for area and perimeter, which we'll explore next.
Rectangle Formulas
Remember
Perimeter is one-dimensional (measured in units), while area is two-dimensional (measured in square units).
Formulas for Common Shapes
Rectangle
Perimeter: 2 × (L + W)
Area: L × W
Square
Perimeter: 4 × S
Area: S × S
Triangle
Perimeter: a + b + c
Area: ½ × b × h
Circle
Circumference: 2πr
Area: πr²
Formula Tip
Always include units in your answer - linear units for perimeter, square units for area!
Real-World Examples
Let's practice with some real-world examples:
Example 1: A rectangular garden is 8m long and 5m wide. What is its perimeter and area?
Perimeter: 2 × (8 + 5) = 2 × 13 = 26m
Area: 8 × 5 = 40m²
Example 2: A square room has sides of 6ft. What is its perimeter and area?
Perimeter: 4 × 6 = 24ft
Area: 6 × 6 = 36ft²
Example 3: A triangular sail has a base of 10m and height of 8m. What is its area?
Area: ½ × 10 × 8 = 40m²
Example 4: A circular pizza has a diameter of 14 inches. What is its area?
Radius = 14 ÷ 2 = 7 inches
Area: π × 7² ≈ 3.14 × 49 ≈ 153.86 in²
Practice calculating area and perimeter for objects around your home!
Measurement Tip
For irregular shapes, break them down into regular shapes whose area you can calculate separately.
Area and Perimeter Quiz
Test your understanding with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about area and perimeter:
Measurement Trivia
Discover interesting facts about area and perimeter:
Ancient Measurements
The concept of area dates back to ancient Egypt, where surveyors called "rope-stretchers" measured land areas after Nile floods using knotted ropes to calculate areas for farming.
Largest Perimeter
The country with the largest perimeter is Canada, with a coastline of 202,080 km! If you walked this distance at 5km/h, it would take over 4.6 years to complete without stopping.
Space Calculations
NASA scientists use area and perimeter calculations to design spacecraft. The solar panels on the International Space Station cover an area of 2,500 m² - enough to cover half a football field!
Largest Area
The largest country by area is Russia, covering 17.1 million km². The smallest is Vatican City at just 0.44 km² - smaller than many college campuses!
