What is the Area of Rectangle?

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

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the area of the square will be equal to the square of side-length.

Area of rectangle = Length x Breadth

A = lb

Area Of Rectangle

Area of Rectangle Formula

The formula to find the area of 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 for 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 in a square-unit dimension. In the case of a square, the area will become side2. The main difference between square and rectangle is that the length and breadth are equal for square.

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 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

\begin{array}{l} L e n g t h = \sqrt{D i a g o n a l^{2} - W i d t h^{2}} \end{array}

(Width)2 = (Diagonal)2 – (Length)2

\begin{array}{l} W i d t h = \sqrt{D i a g o n a l^{2} - L e n g t h^{2}} \end{array}

Now, the area of rectangle = Length × Width

\begin{array}{l} A r e a = L e n g t h \times \sqrt{D i a g o n a l^{2} - L e n g t h^{2}} \end{array}

\begin{array}{l} A r e a = \sqrt{D i a g o n a l^{2} - W i d t h^{2}} \times W i d t h \end{array}

Important Facts

Below are some special formulas related to the rectangle area.
How to find the area with diagonal of rectangle and width

\begin{array}{l} F o r m u l a : A r e a = W i d t h \sqrt{(D i a g o n a l^{2} - W i d t h^{2})} \end{array}

Find a missing side length when the area is known

Formula: Length = Area/Width

Why 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.

Suppose, ABCD is a rectangle.

Area of Rectangle using Length and Breadth

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