Area Of A Rectangle- Definition, Formula, Examples

Safalta expert Published by: Yashaswi More Updated Sat, 09 Sep 2023 11:35 AM IST

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The number of unit squares that can fit into any form is its area. The term "unit" refers to one (1), therefore a unit square is a square having one (1) unit of side. As a result, the area of a rectangle is equal to the number of unit squares within the rectangle's edge. The area of a rectangle, on the other hand, is the space occupied within the rectangle's perimeter. The unit-length tiles in your home are a fantastic illustration of a rectangular form.

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By counting the number of tiles on the floor, you can quickly determine how much area it takes up. This will also assist you in determining the rectangle floor's area. You may also read DefinDefinitionsmulas, and Questions and answers of Speed, Time, and Distance!

 

What is the Area of a Rectangle?

Definition: The area of the rectangle is the area occupied by a rectangle inside its boundaries.

The area of a flat surface of a specific form may be described as the amount of space it covers. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The number of unit squares that can fit into a rectangle is called its area. The flat surfaces of laptop displays, blackboards, painting canvas, and other rectangular forms are examples. The area of a rectangle formula may be used to calculate the space occupied by these items. Consider a rectangle with a length of 4 inches and a width of 3 inches.

Area of rectangle = Length x Breadth
 
A = lb
 
 

Area of Rectangle Formula

The formula to find the area of a rectangle depends on its length and width. The area of a rectangle is calculated in units by multiplying the width (or breadth) by the Length of a rectangle. Lateral and total surface areas can be calculated only for three-dimensional figures. We cannot calculate the rectangle since it is a two-dimensional figure. Thus, the perimeter and the area of a rectangle are given by:

The formula for the Area of a Rectangle
Area of a rectangle
A = l × b
 

The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle’s area will obtain a square-unit dimension. In the case of a square, the area will become a side square. The main difference between a square and a rectangle is that the length and breadth are equal for a square.


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How to Calculate the Area of a Rectangle

Follow the steps below to find the area:

Step 1:  Note the dimensions of length and width from the given data

Step 2: Multiply the length and width values

Step 3: Write the answer in square units
 

Area of Rectangle Using Diagonal

We know that the diagonal of a rectangle is calculated using the formula:

(Diagonal)2 = (Length)2 + (Width)2

From this,

(Length)2 = (Diagonal)2 – (Width)2

Length = √Diagonal2–Width2Diagonal2–Width2

Or

(Width)2 = (Diagonal)2 – (Length)2

Width = √Diagonal2–Length2Diagonal2–Length2

Now, the area of rectangle = Length × Width

Area = Length × √Diagonal2–Length2Diagonal2–Length2

Or

Area = √Diagonal2–Width2Diagonal2–Width2 × Width

You may also read-

 

Important Facts

Below are some special formulas related to the rectangle area:

1. How to find the area with a diagonal rectangle and width

          Formula: Area = Width √(Diagonal2–Width2)Width (Diagonal2–Width2)

2. Find a missing side length when the area is known

           Formula: Length = Area/Width

 

Why the Area of the rectangle is length x breadth?

The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.




 

Now, let diagonal AC divide the rectangle into two right triangles, i.e. ∆ABC and ∆ADC.

We know that ∆ABC and ∆ADC are congruent triangles.

Area of ∆ABC = ½ x base x height =  ½ x AB x BC =  ½ x b x l

Area of ∆ADC = ½ x base x height = ½ x CD x AD =  ½ x b x l

Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC

Area (ABCD) = 2(½ x b x l)

Area (ABCD) = l x b 

Thus, the area of the rectangle = Length x Breadth

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The area of a rectangle is the region covered by the rectangle in a two-dimensional plane in geometry. A rectangle is a type of quadrilateral, a 2D shape that has four sides and four vertices. All four angles of the rectangle are right angles or equal to 90 degrees. The opposite sides of the rectangle are equal and parallel to each other. To be noted, a parallelogram also has its opposite sides equal and parallel to each other but the angles are not equal to 90 degrees. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that students have conceptual clarity in all the subjects and can score their maximum in the exams. You may also read Definitions, Formulas, and Questions and answers about Speed, Time, and Distance!


Table Of Contents-
1. What is the area of a rectangle?
2. Area of a rectangle formula
3. How to calculate the area of a rectangle?
4. Area of  a rectangle using diagonal
5. Important facts
6. Why the area of a rectangle is length in breadth?


 

What is the Area of a Rectangle?

Definition: The area of a rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Essentially, the formula for area is equal to the product of the rectangle's length and breadth. The perimeter of a rectangle, on the other hand, is equal to the total of its four sides. As a result, the region contained by the rectangle's perimeter equals its area. In the case of a square, however, because all of the sides are equal, the area of the square will be equal to the square of the side length.

Area of rectangle = Length x Breadth

 

A = lb

 
 

Area of Rectangle Formula

The formula to find the area of a rectangle depends on its length and width. The area of a rectangle is calculated in units by multiplying the width (or breadth) by the Length of a rectangle. Lateral and total surface areas can be calculated only for three-dimensional figures. We cannot calculate the rectangle since it is a two-dimensional figure. Thus, the perimeter and the area of a rectangle is given by:

The formula for the Area of a Rectangle
Area of a Rectangle A = l × b
 

The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle’s area will obtain a square-unit dimension. In the case of a square, the area will become a side square. The main difference between a square and a rectangle is that the length and breadth are equal for a square.


Related Links-



 

How to Calculate the Area of a Rectangle

Follow the steps below to find the area:

Step 1:  Note the dimensions of length and width from the given data

Step 2: Multiply the length and width values

Step 3: Write the answer in square units


 

Area of Rectangle Using Diagonal

We know that the diagonal of a rectangle is calculated using the formula:

(Diagonal)2 = (Length)2 + (Width)2

From this,

(Length)2 = (Diagonal)2 – (Width)2

Length = √Diagonal2–Width2Diagonal2–Width2

Or

(Width)2 = (Diagonal)2 – (Length)2

Width = √Diagonal2–Length2Diagonal2–Length2

Now, the area of rectangle = Length × Width

Area = Length × √Diagonal2–Length2Diagonal2–Length2

Or

Area = √Diagonal2–Width2Diagonal2–Width2 × Width

You may also read-


 

Important Facts

Below are some special formulas related to the rectangle area:

1. How to find the area with a diagonal rectangle and width

          Formula: Area = Width √(Diagonal2–Width2)Width (Diagonal2–Width2)

2. Find a missing side length when the area is known

           Formula: Length = Area/Width


 

Why the Area of the rectangle is length x breadth?

The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.




 

Now, let diagonal AC divide the rectangle into two right triangles, i.e. ∆ABC and ∆ADC.

We know that ∆ABC and ∆ADC are congruent triangles.

Area of ∆ABC = ½ x base x height =  ½ x AB x BC =  ½ x b x l

Area of ∆ADC = ½ x base x height = ½ x CD x AD =  ½ x b x l

Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC

Area (ABCD) = 2(½ x b x l)

Area (ABCD) = l x b 

Thus, the area of the rectangle = Length x Breadth

 

Area of rectangle Solved Examples

 

Example 1: Find the area of the rectangle whose length is 15 cm and the width is 4 cm.

Solution:

Given,

Length = 15 cm

Width = 4 cm

Area of a rectangle = Length × Width

15 × 4  = 60

So the area of rectangle = 60 cm2

 

Example 2: Find the area of a rectangular blackboard whose length and breadth are 120 cm and 100 cm, respectively.

Solution:

Length of the blackboard = 120 cm = 1.2 m

Breadth of the blackboard = 100 cm = 1 m

Area of the blackboard = area of a rectangle = length x breadth = 1.2 m x 1 m = 1.2 square-metres

What is the formula for area of rectangle?

The formula for the area of a rectangle is:
Area = Length x Breadth

What is the perimeter of rectangle?

The perimeter of the rectangle is the sum of all its four sides. Hence,
Perimeter (rectangle) = 2 (Length + Breadth)

What is the area of rectangle?

The area of the rectangle is the region occupied by the sides of the rectangle.

Why is the area of rectangle LB?

The area of the rectangle is LB because we calculate here the square units of the rectangle. After multiplying the total squares in the length and total squares in the width of the rectangle, will give the total squares in rectangle.

What is the unit of area?

The unit of area of any shape is square. For example, sq.m. or m^2.

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