**Rectangle**

A quadrilateral having opposite sides equal and each angles 90°
(right angle) is called a **rectangle**.

Or, we can say that a rectangle is a parallelogram with each angle 90°. So, each rectangle is a parallelogram but each parallelogram is not a rectangle.

In the given figure of quadrilateral ABCD, opposite sides AB = CD
and AD = BC and each angles ∠A, ∠B, ∠C and ∠D are 90°. So ABCD is a rectangle.

**Length and breadth of
a rectangle**

The longer side of the rectangle is taken as **length**, it is denoted by ‘**l**’. And, the shorter side is taken as **breadth**, and it is denoted by ‘**b**’.

In the given figure of rectangle ABCD,

Length (l) = BC = AD

Breadth (b) = AB = CD

**Diagonals of a
rectangle**

The line joining the opposite vertices of a rectangle or any
polygon is called a **diagonal**. Two diagonals
of a rectangle are equal and bisect to each other.

In the given figure of rectangle ABCD. AC and BD are diagonals. They
are equal and bisect to each other i.e. AC = BD and AO = CO, BO = DO.

The length of diagonal of a rectangle is given by the formula:

Length of diagonal = √(l^{2}
+ b^{2})

**Perimeter and Area of
Rectangle**

The perimeter and area of a rectangle are given by the formula:

Perimeter of rectangle = 2(l + b)

Area of rectangle = l × b

**Properties of
Rectangle**

1.
Opposite sides of a
rectangle are equal.

2.
Each angle of a rectangle
is 90°.

3.
Opposite sides of a
rectangle are parallel.

4.
Diagonals of a rectangle
are equal.

5.
Diagonals of a rectangle
bisect to each other.

**Worked Out Examples**

**Example 1:** Calculate the area and perimeter of the rectangle given below:

**Solution:**

Here,

In the given rectangle ABCD,

Length (l) = 12 cm

Breadth (b) = 5 cm

∴ Area (A) = l × b

= 12cm × 5cm

= 60 cm^{2}

And,

∴ Perimeter (P) = 2(l + b)

= 2(12cm
+ 5cm)

= 2 ×
17cm

= 34cm

∴ Area = 60cm^{2} and Perimeter = 34cm Ans.

**Example 2:** Calculate the area and perimeter of the rectangle given below:

**Solution:**

Here,

In the given rectangle ABCD,

Diagonal (d) = 5cm

Length (l) = 4cm

We know,

l^{2} + b^{2} = d^{2}

i.e. (4cm)^{2}
+ b^{2} = (5cm)^{2}

or, 16cm^{2} +
b^{2} = 25cm^{2}

or, b^{2} =
25cm^{2} – 16cm^{2}

or, b^{2} = 9cm^{2}

or, b = √(9cm^{2})

or, b = 3cm

Now,

Area (A) = l × b

= 4cm × 3cm

= 12 cm^{2}

And,

Perimeter (P) = 2(l + b)

= 2(4cm
+ 3cm)

= 2 × 7cm

= 14cm

∴ Area = 12cm^{2} and Perimeter = 14cm Ans.

If you have any questions or problems regarding the **Rectangle**, you can ask here, in the comment section below.

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