Area of a Rectangle – How to Calculate Area and Perimeter of Rectangle?

# Area of a Rectangle – How to Calculate Area and Perimeter of Rectangle?

A rectangle is a four sided geometric figure in which there are four interior angles each equal to a right angle (90°).

Or, A rectangle can also be considered as a quadrilateral with 4 right angles. parallelogram with four right angles. Therefore, the rectangle is also known by the name of equiangular quadrilateral.

Note : It is very interesting to note that although, all rectangles are parallelograms, but not all the parallelograms are rectangles.

Here, Rectangle with vertices ABCD can be denoted as rect. ABCD.

A rectangle has its sides named, length (L) and breadth (B). Both the length and breadth are different in size. But, the opposite sides of length and breadth are congruent.

Like, in the above shown rectangle, length AB is equal to length CD and breadth BC is equal to breadth DA.

## Learning about the the shape of Rectangle :-

A rectangle is a 2-D figure and has a flat shape. In a 2-D plane, YZ, we can easily represent a rectangle, where the arms of y-axis and z-axis are the length and breadth of the given rectangle.

## Rectangular shaped objects around us :-

In our daily life, we come across many objects which are rectangular in shape. Some of the most common everyday rectangular things or objects which we perceive in our daily life are Television and Computer screen, Books and Copies, Screen of mobile phones, Notice boards, Table, Book, Wall, Tennis court, etc.

## Facts and information about Rectangle :-

• All rectangle has four sides and four vertices.

• The opposite sides of the rectangle are equal in length and thus congruent.

• Each vertex of the rectangle has an interior angle equal to 90 degrees.

• when the sum of all the interior angles of the rectangle taken it comes out to be 360°.

• There are two diagonals in a rectangle and both the diagonals bisect each other.

## Understanding the Perimeter of Rectangle :-

Peter wanted to surround his field, which was rectangular in shape with barbed wire from all the four sides.

He asked his friend John to suggest him the method by which he can get the exact amount of wire needed for this. John suggested Peter to calculate the perimeter of the field.

Therefore, the perimeter of a rectangle has been defined as the total distance covered by its outer boundary. Since, In a rectangle there are four sides, thus, its perimeter will be equal to the sum of the four sides. The perimeter is measured in unit length.

The formula to calculate the perimeter is given by:

We learnt that the perimeter of the rectangle is equal to the sum of its 4 sides.

Hence, perimeter (P) is;

P = sum of all its four sides

P = AB + BC + CD + DA

P = AB + BC + AB + BC  (Opposite sides of rectangle are equal)

P = 2( AB  +  BC)

Here, AB is the length (l) and BC is the breadth (b) of the rectangle.

Hence, Perimeter (P) = 2(l+b) Units.

1. The length and breadth of Lyca Math’s book are 7 cm and 12 cm, respectively. Then, find the perimeter of her book.

Solution :-

Given: Length of Lyca book = 7 cm

Width of Lyca book = 12 cm

We learnt that,

The perimeter of a rectangle = 2(length + breadth)

Perimeter, P = 2(7 + 12) cm

P = 2 x 19 cm

Therefore, the perimeter of Lyca book is equal to 38 cm.

2.  A rectangular garden has length equals to 12 cm and perimeter equals to 80 cm. Find its breadth.

Solution :-

Given, Perimeter of the garden = 80 cm

Length of the yard = 12 cm

Let B be the breadth of the given garden.

From the formula, we know,

Perimeter, P = 2(length + breadth)

Substituting the values, we get;

12 + W = 40

B = 40 – 12 = 28 cm

Hence, the breadth of the given rectangular garden is equal to 28 cm.

## Do it yourself :-

1. Find the perimeter of a given rectangle which has length = 28 cm and breadth = 36 cm.

2. Joseph has a rectangular grassland whose perimeter is equal to 150 cm and breadth equal to 25 cm. Then, find the length of the grassland.

3. Find the perimeter of a rectangular yard whose length is 30 cm and breadth is two times the length.

4. If it is given that the diagonal of a rectangular box is 5 cm and its length is 4 cm. Then find its breadth and thus the perimeter of the rectangle.

5. A box is rectangular in shape and it length and breadth are in the ratio 5 : 3. If its perimeter is 168 cm, find its length and breadth.

6. There is a rectangular box in Syra room whose length and breadth are 16 cm and 12 cm respectively. Find its perimeter if the length and breadth are (i) Triples (ii) One-halved

## Learning about the Area of Rectangle

Ariana wanted to cover the floor of her room, which was rectangular in shape with carpet. She asked her sister about the method using which she can calculate the exact amount of needed carpet. Her mother suggested calculating the area of the floor.

Thus, the area of a rectangle is the region covered by it within its four sides or boundaries. It is measured in square units.

The formula to find the area of a rectangular figure depends on its length and breadth. The area of a rectangle is calculated by multiplying its length by breadth.

Thus, the area of a rectangle = length × breadth

Area of a Rectangle (A) = l × b unit²

1.  Jenny measured her book which is rectangular in shape and found the length to be 19 cm and the breadth to be 4 cm. Then, find the area of Jenny book.

Solution:

Given, Length of the book = 19 cm

Breadth of the book = 4 cm

We learn, area of Rectangle = Length × breadth

= 19 × 4  = 76

So, the area of Jenny book is equal to 76 cm²

2. If the length of a rectangular blackboard is 16 cm. Its area is 160 cm². Find its breadth.

Solution:

Given,

Area of the blackboard = 180 cm²

Length of the blackboard = 15 cm

We learnt, area of Rectangle = length x breadth

Now, breadth of rectangle = area/length

Thus, the breadth of the given rectangular screen is 160/16 = 10 cm.

3. If the diagonal of a rectangular sheet is equal to 5 cm and its breadth is equal to 4 cm, then find its length and thus the area of the sheet.

Solution:

Given,

Diagonal of the sheet = 5 cm

Breadth of the sheet = 4 cm

We know that,

(5)² = (l)² + (4)².

(l)² = 25 – 16

(l)² = 9 cm

l = 3 cm

The length of the rectangle is equal to 3 cm.

Now, we know that the area of a rectangle is l × b

Thus, Area = 3 cm × 4cm

= 12 cm²

## Do it yourself :-

1.The area of a rectangular fence is 600 square feet. If the width of the fence is 10 feet, then find its length.

2. A rectangular floor whose length and breadth is 40 m and 30 m respectively needs to be covered by rectangular tiles. If it is given that the dimension of each tile is 3 m x  4m. Find the total number of tiles that would be required to cover the floor fully.

3. If the area of a rectangular box is measured as 1444 cm². If its length is 35 cm, find its breadth.

4. The diagonal of a rectangle is 16 cm². If the length of one diagonal is 4 cm. Then, find its breadth and thus the area of the rectangle.

5. If the length and breadth of a given rectangular television screen is in a ratio of 4:3 and its area is 14147cm². Then, find the length and breadth of the television screen.