Perimeter of Rectangle

Introduction  

Understanding the perimeter of a rectangle is basic in geometry and everyday uses like construction, fencing, and design. The perimeter helps find the total boundary length, which is important for solving real-world problems. This topic will cover the definition, the perimeter of a rectangle formula, how to find the perimeter of a rectangle, and also look into rectangle properties, derivations, and practical examples.  

 

Table of Contents

• What is Perimeter of Rectangle?
• Perimeter of Rectangle Formula
• How to Find the Perimeter of a Rectangle
• Derivation of Perimeter Formula
• 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 length around its edges. It measures the outer boundary using the lengths of its sides.  

A rectangle is a quadrilateral with equal opposite sides and all angles at 90 degrees. Therefore, the Length and width of rectangle are enough to calculate its perimeter. In short, the perimeter is the sum of all its sides.  

 

Perimeter of Rectangle Formula  

To find the perimeter of a rectangle, we use this basic formula:  

Perimeter of Rectangle = 2 × (Length + Width)  

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

 

How to Find the Perimeter of a Rectangle?  

1. Measure the length of the rectangle.  

2. Measure the width of the rectangle.  

3. Apply the perimeter formula:  

   Perimeter of Rectangle = 2 × (Length + Width)  

By following these steps, you can learn how to find the perimeter of a rectangle

for any given values.  

 

Derivation of Perimeter Formula  

The perimeter formula comes from the basic properties of rectangles:  

• Opposite sides are equal in length.  
• There are two pairs of equal sides: 2 × Length and 2 × Width.  
  

So, the perimeter is calculated as:  

Perimeter = Length + Width + Length + Width  

                 = 2 × (Length + Width)  

This derivation reinforces the concept of rectangle properties in geometry.  

 

Area of a Rectangle

While the perimeter measures the boundary, the area measures the surface it covers.  

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. 

 

These properties directly influence how we use the perimeter formula.  

 

Solved Examples on Perimeter of Rectangle  

Example 1  

Given: Length = 10 cm, Width = 5 cm  

Find the perimeter of the rectangle.  

Perimeter = 2 × (10 + 5) = 2 × 15 = 30 cm  

 

Example 2  

Given: Length = 7.5 m, Width = 3.5 m  

Find the perimeter of the rectangle.  

Perimeter = 2 × (7.5 + 3.5) = 2 × 11 = 22 m  

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.  

 

Related Links

Rectangle - Explore the properties of rectangles, including sides, angles, perimeter, and area, with diagrams and real-life examples.

Area of Trapezium - Learn how to calculate the area of a trapezium using formulas, with step-by-step examples and visual aids.

 

Frequently Asked Questions on Perimeter of Rectangle  

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

Ans: 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?  

Ans: 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?  

Ans:  

   Perimeter = 2 × (Length + Width)  

   = 2 × (4 + 6)  

   = 2 × 10  

   = 20 cm  

 

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

Ans:  

   Perimeter = 2 × (Length + Width)  

   = 2 × (8 + 5)  

   = 2 × 13  

   = 26 cm  

Learn more math concepts at Orchids The International School.