Rectangle

A Rectangle is a four sided-quadrilateral having all the internal angles to be right-angled (90o).

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

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

Rectangle

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-

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

List of Properties of Rectangle:

To understand the properties of a rectangle, let’s learn what is a rectangle first. As we have seen many different shapes which are either 2 dimensional or 3 dimensional and so on. Out of these shapes, Rectangle is an important two-dimensional shape. It is a four-sided polygon. All the four sides are straight with four right angles i.e each angle is a right angle in a rectangle. The most common everyday things we see and is rectangular in shape is Television, computer screen, notebook, mobile phones, CPU , Notice boards etc.

  • It’s a parallelogram with four right angles.
  • It’s diagonals bisect each other.
  • The opposite side of  a rectangle is equal.
  • The opposite side of the rectangle is parallel.
  • The area of a recangle is = l x b, where l = length and b = breadth.
  • The perimeter of a rectangle is 2(l + b ).
  • The sum of all the interior angle of a rectangle is 3600
  • The diagonal of a recatngle acts like a diameter of its circumference.

Diagonal of a Rectangle-

Rectangle- Diagonals

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

\(\Rightarrow D = \sqrt{12^{2}+8^{2}}\)

\(\Rightarrow D = \sqrt{144 + 64} \)

\(\Rightarrow D = \sqrt{208} \)

\(\Rightarrow D = 4\sqrt{13}\)

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Practise This Question

Express 32000 as a product of powers of prime factors.