The Perimeter and Area of Rectangle are two important formulas in **Mensuration**. It calculates the space occupied by the rectangle and the length of boundaries of the rectangle. In this article, students can come across the concept of area and perimeter of rectangle deeply.

A rectangle is a quadrilateral with two equal sides and two parallel lines and four right angles. The concept of area and perimeter of rectangle formulas are explained with examples. Some of the examples of different shapes are given below.

## What is Perimeter and Area of a Rectangle?

**Perimeter:** Perimeter of the rectangle is the sum of all the sides of the rectangle. The rectangle has two lengths and two breadths. To find the perimeter of the rectangle we have to add the length and breadth. It is measured in units. It is denoted by P.

**Area:** The area of the rectangle formula helps to calculate the length and breadth of the two-dimensional closed figure. To find the area of the rectangle we have to multiply the length and breadth of the rectangle. It is measured in square units. It is denoted by A.

### Properties of Rectangle

- A Rectangle has two equal sides
- The rectangle is a quadrilateral
- The diagonals of the rectangle have the same length.
- The diagonal of the rectangle bisect each other.
- Sum of all the four angles is 360º
- Each angle of the rectangle is 90º
- If the sides of the rectangle are l and b then the diagonal of the rectangle d = √l² + b²
- The opposite sides of the rectangle are parallel.

### Derivation of Perimeter of a Rectangle

The perimeter of the rectangle is the sum of all four sides.

P = l + l + b + b

P = 2l + 2b

P = 2(l + b)

Thus the perimeter of the rectangle is = 2(l + b)

### Area of the Rectangle

The area of the rectangle is the product of length and breadth.

A = l × b

### Perimeter and Area of Rectangle Formula

- Area of Rectangle = l × b
- Perimeter of Rectangle = 2(l + b)
- Length of the rectangle = A/b
- The breadth of the Rectangle = A/l
- Diagonal of the Rectangle = √l² + b²

### Solved Problems on Area and Perimeter of a Rectangle

The formula of Perimeter and Area of Rectangle is explained step by step here with examples. Go through the below questions and solve the problems using the Area and Perimeter of the Rectangle formula.

**1. Find the length of the rectangular plot whose breadth is 11 cm and the area is 165 cm². Also, find the perimeter of the rectangle?**

Solution:

Given,

Breadth = 11 cm

Area = 165 cm²

Area of the rectangle = l × b

165 sq. cm = l × 11 cm

l = 165/11

l = 15 cm

Thus the length of the rectangle is 15 cm.

We know that,

Perimeter of the rectangle = 2(l + b)

P = 2(15 + 11)

P = 2(26)

P = 52 cm

Thus the perimeter of the rectangle is 52 cm.

**2. Find the Perimeter of the Rectangle whose length is 10 cm and breadth is 8 cm?**

Solution:

Given, Length = 10 cm

Breadth = 8 cm

We know that,

Perimeter of the rectangle = 2(l + b)

P = 2(10 cm + 8 cm)

P = 2(18 cm)

P = 36 cm

Therefore the perimeter of the rectangle is 36 cm.

**3. Find the area of the rectangle whose length is 14 meter and width is 10 meters?**

Solution:

Given,

Length = 14 meter

Width = 10 meter

We know that,

Area of the rectangle = l × w

A = 14 m × 10 m

A = 140 sq. meters

Therefore the area of the rectangle is 140 square meters.

**4. A rectangular plot has its length of 16 cm and a perimeter of 60 cm. Find the width of the rectangular plot?**

Solution:

Given,

Length = 16 cm

Perimeter = 60 cm

Width = ?

We know that

The perimeter of the rectangle = 2(l + w)

60 cm = 2(16 cm + w)

16 + w = 60/2

16 + w = 30

w = 30 – 16

w = 14 cm

Thus the width of the rectangular plot is 14 cm.

**5. Find the area and perimeter of the rectangle whose length and breadth are 12 m and 6 m?**

Solution:

Given,

length = 12 m

breadth = 6 m

We know that,

Area of the rectangle = l × b

A = 12 m × 6 m

A = 72 sq. meters

Now find the perimeter of the rectangle

P = l + l + b + b

P = 12 m + 12 m + 6 m + 6 m

P = 24 m + 12 m

P = 36 m

Therefore the area and perimeter of the rectangle is 72 square meters and 36 meters.

### FAQs on Area and Perimeter of Rectangle

**1. How to find the perimeter of a rectangle?**

The perimeter of the rectangle can be calculated by adding all the sides of the rectangle.

**2. What is the area of the rectangle?**

The area of the rectangle is defined as the space occupied by the rectangle or closed figure. It is the product of length and breadth.

**3. What is the unit for the perimeter of a rectangle?**

The unit for the perimeter of the rectangle is cm or meters.