A Rectangle is a four sided-quadrilateral having all the internal angles to be right-angled (\(90^{\circ}\)).

It is to be noted that in a rectangle the opposite sides are equal in length which makes it different from aÂ square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

A rectangle is characterized by length (L) and width (W). Both length and width are different in size.

In the figure above, a rectangle ABCD has four sides as AB, BC, CD, and DA and right angles A, B, C, and D. The distance between A and B or C and D is defined as the length (L), whereas the distance between B and C or A and D is defined as Width (W) of the given rectangle.

**Real world application of Rectangles:**

Table, Book, TV screen, Mobile phone, Wall, Magazine, Tennis court, etc.

**Perimeter of a Rectangle:**

The perimeter is defined as the total distance around the surface.

Mathematically Perimeter is given as-

\(P = 2(Length + Width)\) unit length

**Area of Rectangle:
**Before calculating the area of a rectangle, let us know what exactly an area is. An area is a way of measuring how much space is contained inside a particular figure.

Mathematically, it is given as-

\(A = Length \times Width \;\; unit^{2}\)

**Properties of a Rectangle:**

(i) The opposite sides are equal and parallel.

(ii) The diagonals are congruent.

(iii) Each of the interior angles of a rectangle is \(90^{\circ}\) making the sum of interior angle to be \(360^{\circ}\).

**Diagonal of a Rectangle-**

A rectangle has two diagonals, they are equal in length and intersect in the middle.

**Length of Diagonals-**

The length of diagonals can be found using the Pythagoras Theorem–

\(D = \sqrt{L^{2}+W^{2}}\)

Example- Find the Area and Perimeter of a rectangle where length and width are given as 12 and 8 cm respectively. Also, find the length of the Diagonal.
Solution- We know that the area of a rectangle is given by \(A = Length \times Width\). \(\Rightarrow A = 12 \times 8\) \(\Rightarrow A = 96 cm^{2}\) Now Perimeter is given by \(P = 2 (Length + Width) \) \(\Rightarrow P = 2 (12 + 8) \) \(\Rightarrow P = 40 \) Diagonal Length, \(D = \sqrt{L^{2}+W^{2}}\) \(\Rightarrow D = \sqrt{12^{2}+8^{2}}\) \(\Rightarrow D = \sqrt{144 + 64} \) \(\Rightarrow D = \sqrt{208} \) \(\Rightarrow D = 4\sqrt{13}\) |