Perimeter

 

Perimeter is a very useful concept in mathematics that we apply in daily life without even realizing it. For example, if you want to fence your garden, measure a running track, or decorate the edge of a table with ribbon, you are actually calculating the perimeter.

 

Table of Contents

• What is Perimeter?

• How to Find Perimeter?

• Perimeter Units

• Perimeter Formula

• Difference Between Perimeter and Area

• Solved Examples on Perimeter

• Fun Facts about Perimeter

• Common Misconceptions about Perimeter

• Practice Questions

• FAQs on Perimeter
  
  

What is Perimeter?

The perimeter of a shape is the total length of the boundary of any closed two-dimensional figure. It is the distance covered around the shape.
For example, if you have a square-shaped farm and know the length of one side, multiplying it by 4 gives the total length of the fencing needed, i.e., the perimeter.

How to Find Perimeter?

To calculate the perimeter, add up the lengths of all sides of the figure.
Example: A rectangular farm has length lll and breadth bbb.

Perimeter of rectangle=2(l+b)\text{Perimeter of rectangle} = 2(l+b)Perimeter of rectangle=2(l+b)

This formula works because opposite sides are equal and we sum all sides.

Perimeter Units

Since perimeter measures length, it is always expressed in linear units such as:

• Meters (m), centimeters (cm), kilometers (km)

• Inches (in), feet (ft), yards, miles
  
  

Unlike area (which is in square units), perimeter is one-dimensional.

 

Perimeter Formula

The general formula:

Perimeter=Sum of all sides\text{Perimeter} = \text{Sum of all sides}Perimeter=Sum of all sides

 

Difference Between Perimeter and Area

• Perimeter: length of the boundary (measured in units).

• Area: amount of surface covered inside the boundary (measured in square units).
  
  

Example with a rectangle:

• Perimeter = 2(l+b)2(l+b)2(l+b)

• Area = l×bl \times bl×b
  
  

 

Solved Examples on Perimeter

Q1. Find the perimeter of a square with side 5 m.
Solution: P=4a=4×5=20P = 4a = 4 \times 5 = 20P=4a=4×5=20 m.

Q2. A rectangle has length 8 cm and breadth 6 cm. Find its perimeter.
Solution: P=2(l+b)=2(8+6)=28P = 2(l+b) = 2(8+6) = 28P=2(l+b)=2(8+6)=28 cm.

Fun Facts about Perimeter

• The word “perimeter” comes from Greek peri (around) and metron (measure).

• Running tracks, circular parks, and picture frames are real-life examples of perimeter.

• Two different shapes can have the same perimeter but different areas.
  
  

Common Misconceptions about Perimeter

•  Misconception: Perimeter and area are the same.
    Truth: Perimeter is length around, while area is surface inside.

•  Misconception: Units of perimeter are always in square units.
  Truth: Perimeter uses normal length units (m, cm, ft).
  
  

Practice Questions

1. Find the perimeter of a triangle with sides 7 cm, 8 cm, and 5 cm.

2. A circular garden has radius 14 m. Find its perimeter.

3. A square field has perimeter 64 m. Find its side length.

4. Which has a larger perimeter: a square of side 10 cm or a rectangle of length 12 cm and breadth 8 cm?

5. A wire of length 36 cm is bent into a rectangle of sides 10 cm and 8 cm. Is the perimeter correct?
   
   

Frequently Asked Questions on Perimeter

Q1. What is the perimeter in simple words?

 Answer: The total length of the boundary of a closed shape.

Q2. How is perimeter different from area?

Answer: Perimeter is measured in units (m, cm, ft), while area is measured in square units (m², cm², ft²).

Q3. What is the perimeter formula of a circle?

Answers: 2πr2\pi r2πr, where rrr is radius.

Q4. Can two shapes have the same perimeter but different areas?

Answer: Yes, for example, a square and a rectangle may have equal perimeters but different areas.

Q5. Why is perimeter important?

Answer: It helps in real-life situations like fencing land, framing pictures, or laying boundaries.

 Explore more math concepts like Area and Perimeter worksheets and Perimeter of Shapes practice problems at Orchids The International School.