Perimeter of Rectangle

Introduction  

Learning about the perimeter of a rectangle is one of the basics in geometry. The perimeter simply means the total distance around the rectangle. It tells us how long the boundary is if we walk all the way around it. This idea is not only useful in maths but also in real life, like when building a fence, designing a room, or measuring land.

In this guide, we will learn what the perimeter of a rectangle means, understand its formula, walk through the step-by-step calculation, explore rectangle properties, and examine some simple practical examples.

 

Table of Contents

• What is Perimeter of Rectangle?
• Perimeter of Rectangle Formula
• How to Find the Perimeter of a Rectangle
• Area of Rectangle
• Applications of Perimeter
• Properties of Rectangle
• Solved Examples
• Practice Questions
• Conclusion
• FAQs On Perimeter of Rectangle

 

What is Perimeter of Rectangle?  

The perimeter of a rectangle is the total distance around its edges. In simple words, it is the length of the outer boundary of the rectangle. If you start from one corner and walk all the way around it until you return to the same point, the distance you have covered is called the perimeter. A rectangle is a quadrilateral with opposite sides equal and all angles at 90°. That means we only need the length and the width to calculate its perimeter. In short, the perimeter is the sum of all four sides

 

Perimeter of a Rectangle Formula  

The perimeter of a rectangle is the sum of all its sides. In general, the perimeter of any polygon is the total distance around its boundary.

For a rectangle:

Opposite sides are equal.

So, the perimeter = twice the length + twice the width.

It is usually denoted by P.

Derivation of the Perimeter of a Rectangle

Suppose a rectangle has:

Length = a

Breadth (width) = b

Sum of all sides = a + b + a + b

Simplifying, we get:

P=2(a+b)

where:

• a = length of the rectangle
• b = breadth (width) of the rectangle

So, the perimeter formula is:

Perimeter of Rectangle=2×(Length+Width)

This formula is important in math and practical situations. Once you know the Length and width of a rectangle, you can put the values into the formula to get the result.  

 

How to Find the Perimeter of a Rectangle?  

A rectangle's perimeter is the distance all the way around its edges. To calculate it, we only need two measurements: the length (L) and the width (W) of the rectangle. 

Here's a step-by-step method to work it out:

Step 1: Determine the length and width
Examine the rectangle and determine its length (the longer side) and width (the shorter side). For instance, in a rectangle on a notebook or an actual item such as a table or garden, measure the sides accurately. 

Step 2: Use the perimeter formula
The perimeter of a rectangle is calculated by:

P=2×(Length+Width)

This is from the fact that a rectangle has two equal lengths and two equal widths, so we add all four sides together.

Step 3: Substitute the values
Insert the length and width you calculated into the formula.

Step 4: Add and multiply
First, add the length and width together. Then, multiply the result by 2 to get the total perimeter.

Example:
Let's say a rectangle has:

Length = 8 units

Width = 5 units

P=2×(8+5)=2×13=26 units

Therefore, the perimeter of the rectangle is 26 units.

 

By following these steps, you can learn how to find the perimeter of a rectangle for any given values.  

 

Area of a Rectangle

The area of a rectangle is the amount of space covered inside the rectangle. In simple words, it tells us how much surface the rectangle occupies.

What You Need to Know:

To calculate the area, we only need two measurements:

• Length (L) - the longer side of the rectangle
• Width (W) - the shorter side of the rectangle

Formula for Area:

Area of Rectangle = Length × Width  

This quick reference helps distinguish between the perimeter and area—two different yet related concepts.  

 

Applications of Perimeter of Rectangle  

The perimeter is widely used in real life:  

• Fencing a garden: Helps decide how much material is needed.  

• Constructing frames: Helps in calculating boundary lengths.  

• Architecture: Useful for design elements based on rectangle properties.

Knowing how to find the perimeter using the formula is crucial in these fields. These examples show how geometry affects daily life.  

 

Properties of Rectangles  

To better understand the perimeter, knowing the properties of rectangle is essential:  

• Opposite sides are equal.  

• All interior angles are right angles.  

• Diagonals bisect each other.  

• Length and width of rectangle are enough to find both the area and perimeter.  

These properties directly influence how we use the perimeter formula. 

 

Solved Examples on Perimeter of Rectangle  

Example 1:

Find the perimeter of a rectangle whose length and width are 5 cm and 10 cm, respectively.

Solution:

Given:
Length = 5 cm and Width = 10 cm

We know,
The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(5 + 10) cm

P = 2 x 15 cm

Therefore, the perimeter of a rectangle = 30 cm

 

Example 2:

Find the perimeter of a rectangle whose length is 12 m and width is 7 m.

Solution:

Given:
Length = 12 m and Width = 7 m

We know,
The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(12 + 7) m

P = 2 x 19 m

Therefore, the perimeter of a rectangle = 38 m

 

Example 3:

A rectangular garden has a length of 20 m and a width of 15 m. Find its perimeter.

Solution:

Given:
Length = 20 m and Width = 15 m

We know,
The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(20 + 15) m

P = 2 x 35 m

Therefore, the perimeter of the garden = 70 m

 

Example 4:

Find the perimeter of a rectangle whose length is 18 cm and width is 9 cm.

Solution:

Given:
Length = 18 cm and Width = 9 cm

We know,
The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(18 + 9) cm

P = 2 x 27 cm

Therefore, the perimeter of the rectangle = 54 cm

These examples show how to find the perimeter using the formula in various units.  

 

Practice Questions  

Try solving these using the perimeter formula:  

1. Length = 12 cm, Width = 8 cm. Find the perimeter of the rectangle.  

2. A rectangle has a perimeter of 60 m. If the length is 20 m, what is the width?  

3. Length and width of the rectangle are 9 m and 6 m. What are the area and perimeter?  

4. A rectangle has an area of 56 sq. m and a width of 7 m. What is the perimeter?  

5. Prove the perimeter formula using the rectangle properties.  

These problems test your understanding of the perimeter, how to apply the formula, and how to distinguish between area and perimeter.  

 

Conclusion  

The perimeter of a rectangle is a basic concept in geometry, useful in both school and everyday situations. Knowing the formula, how to find the perimeter of a rectangle, and recognizing rectangle properties helps you approach problems involving rectangular shapes with confidence. Whether calculating boundary lengths or using geometric principles, understanding the perimeter is essential.  

 

Frequently Asked Questions on Perimeter of Rectangle  

1. What is the formula for the perimeter of a rectangle?  

Answer: The formula to calculate the perimeter is:  

   Perimeter = 2 × (Length + Width)  

   This formula adds the lengths of all four sides, where opposite sides are equal.  

 

2. What is the area of a rectangle?  

Answer: The area is found by multiplying length and width.  

   Formula: Area = Length × Width  

   Example: If length = 8 cm and width = 5 cm, then  

   Area = 8 × 5 = 40 cm²  

 

3. What is the perimeter if length = 4 cm and width = 6 cm?  

Answer:  

   Perimeter = 2 × (Length + Width)  

   = 2 × (4 + 6)  

   = 2 × 10  

   = 20 cm  

 

4. What is the perimeter if length = 8 cm and width = 5 cm?  

Answer:  

   Perimeter = 2 × (Length + Width)  

   = 2 × (8 + 5)  

   = 2 × 13  

   = 26 cm  

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