Area Of A Rectangle- Definition, Formula, Examples

What is the Area of a Rectangle?

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

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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.


Related Links-

• Volume Of A Sphere
• CM To Inches (cm to in) Converter
• Roman Numeral Conversion 

 

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-

• Perimeter of a rectangle
• Area of a square

 

Important Facts

Below are some special formulas related to the rectangle area:

          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

You may also read-

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-

• Volume Of A Sphere
• CM To Inches (cm to in) Converter
• Roman Numeral Conversion 

 

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-

• Perimeter of a rectangle
• Area of a square

 

Important Facts

Below are some special formulas related to the rectangle area:

          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