**What is Rectangle?**

Rectangle is a quadrilateral in which **opposite sides are equal** and** all angles measure 90 degrees**

**Keyword for Rectangle**

(a) Opposite sides are equal

(b) All angles measure 90 degree

**Structure of Rectangle**

Rectangle consists of following components

**(a) Length **

The** longest side** in the rectangle is called Length

Here AB & CD are the lengths of rectangle

**(b) Breadth**

The **shorter side** is called Breadth

here BC & AD are the breadths of rectangle

**(c) Vertex**

The **point where two sides join** is called Vertex

A Rectangle has four vertex A, B, C & D

**(d) Angles**

There are four angles in rectangle.**All angle measures 90 degree**.

∠A = ∠B = ∠C = ∠D = 90 degree

**Examples of Rectangle**

**Properties of Rectangle**

**(a) Opposite sides are equal**

Given above is the rectangle ABCD

Here,

AB = CD = 3 cm

AD = BC = 2 cm

**(b) All interior angle measures 90 degree**

In the above rectangle ABCD, all angle measure 90 degrees**∠A = ∠B = ∠C = ∠D = 90 degree**

**(c) Both the diagonals of rectangle have same length**

AC & BD are the diagonals.

According to Rectangle Property: AC = BD

**(d) In Rectangle, diagonals bisect each other**

When lines bisect each other it means that the lines divides into equal halves.

Hence,

AO = OC

DO = OB

**(e) Length of Diagonal of Rectangle**

Formula for length of diagonal of rectangle is:

d\ =\sqrt{a^{2} +b^{2}}

**Proof**

Given above is the triangle ABCD with diagonal BD

Length of rectangle = a cm

Breadth of Rectangle = b cm

Observe triangle BCD is a right triangle**Applying Pythagoras Theorem **

d^{2} =\ \ a^{2} +b^{2} \\\ \\ d\ =\sqrt{a^{2} +b^{2}}

**Hence Proved**

**(f) Diagonals of rectangle bisect at different angles**

In the intersection of diagonals you will find two angle of intersection. One angle will be acute and other will be obtuse.

Given above is rectangle PQRS with diagonals PR & QS intersecting at point O.

The two intersection angles are 52 and 128 degree

**(f) Perimeter of Rectangle**

Perimeter is the** total length of the boundary**.

In Rectangle;

Perimeter = Length + Breadth + Length + Breadth**Perimeter = 2 x ( Length + Breadth)**

**(g) Area of Rectangle**

The region covered by the figure is called Area

In Rectangle;**Area = Length x Breadth**

**(h) Rectangle’s line of symmetry**

Line of symmetry is a** line which divides the geometrical figure into two equal halves.**

In Rectangle, there are **two lines of symmetry**

**(i) Rectangle Circumcircle**

A **circle which touches all the vertex of geometrical figure** is called circumcircle.

In rectangle, the center of the **circumcircle is located at the intersection of diagonals**

Given above is rectangle ABCD with diagonal AC & BD.

The diagonals intersected at point O which is also the center for the circumcenter.

From point O, you can easily draw circle which will touch all the vertex of rectangle.

**Radius of Circumcenter**

Radius of circumcenter = half of diagonal**Radius of circumcenter = ( d / 2 )**

## Frequently asked Questions – Rectangle

**(01) How is Square and Rectangle are different?**

(a) In square all sides are equal while in Rectangle opposite sides are equal.

(b) In square, diagonals intersect at 90 degrees while in rectangle diagonals intersect at different angles

**(02) Is Rectangle a parallelogram?**

Properties of Parallelogram are:

(a) Opposite sides are parallel & equal

(b) Opposite angles are equal

Both the condition applies for rectangle.

Hence rectangle is form of parallelogram

**(03) How are rectangle and parallelogram different?**

In rectangle, all angles are 90 degree.

The same is not the case with parallelogram

**(04) Any real life example of rectangle?**

**Questions on Rectangle**

**(01) Find the area of following rectangle**

**Solution**

Length of Rectangle = 6 cm

Breadth of Rectangle = 3 cm

We know that:

Area of rectangle = Length x Breadth

Area of Rectangle = 6 x 3 sq. cm = 18 sq. cm

**Hence, 18 sq. cm is the area of above image**‘

**(02) Find the area of rectangle of the length is 10 cm and the breadth is 5 cm **

**Solution**

Length of rectangle = 10 cm

Breadth of rectangle = 5 cm

Area of Rectangle = Length x Breadth

Area of Rectangle = 10 x 5 = 50 sq. cm

**Hence, 50 sq. cm is the solution**

**(03) Find the perimeter of the below rectangle**

**Solution**

Length of rectangle = 5 cm

Breadth of rectangle = 3 cm

Perimeter of rectangle = 2 ( Length + Breadth)

Perimeter of rectangle = 2 (5 + 3) = 16 cm

**Hence, 16 cm is the solution**

**(04) The length and diagonal of rectangle is 4 cm and 5 cm respectively. Find the breadth of the rectangle**

We have already discussed the formula for diagonal as:

d^{2} =\ \ length^{2} +breadth^{2}\\\ \\ 5^{2} =\ \ 4^{2} +breadth^{2}\\\ \\ 25\ =\ 16\ +\ breadth^{2}\\\ \\ breadth^{2} \ =\ 9\\\ \\ breadth\ =\ 3\

**Hence, breadth of rectangle is 3 cm**

**(05) A rectangle if formed by joining two squares of side 2 cm. Find the area of rectangle**

When two squares of 2 cm are joined it will produce rectangle of length 4 cm and breadth 2 cm

Length of rectangle = 4 cm

Breadth of rectangle = 2 cm

Area of Rectangle = Length x Breadth

Area of Rectangle = 4 x 2 = 8 sq. cm

**Hence, 8 sq. cm is the solution**