# What is a Rectangle

By the end of this lesson, you will be able to

- define rectangle.
- calculate the perimeter of a rectangle.
- determine the diagonal of a rectangle.
- evaluate the area of a rectangle.
- relate rectangle to parallelogram.
- demonstrate examples of scalene triangle.

## Rectangle

A rectangle is a quadrilateral in which all four interior angles are right angles. It is a special type of parallelogram with a right angle.

A rectangle is showing its sides and angles.

All interior angles are equal to 90°. So it is sometimes called an equiangular quadrilateral.

The two pair of opposite sides of a rectangle are equal to each other.

The opposite sides of a rectangle are also parallel to one another. If the length of the sides of a rectangle were equal, it would be a square.

## Apps for Finding Area, Perimeter and Diagonal

Perimeter:

Area:

Diagonal:

Select button and then drag the pink area on bottom right corner and see the change.

## Rectangle Formula

All the formulae are used generally of rectangle are given below:

## Perimeter of Rectangle

The sum of the length of the total sides of a rectangle is called the perimeter of rectangle. So, the perimeter of a rectangle means the total length of outline of a rectangle. As the opposite sides of a rectangle are of equal length, the perimeter of a rectangle is can be calculated by multiplying 2 the sum of a pair of adjacent sides.

### Perimeter of Rectangle Formula

Let AB = CD = a be the length and BC = AD = b be the width of a rectangle ABCD.

If the perimeter is P,

P = (AB + BC + CD + AD) unit

or, P = (a + a+ b + b) unit

or, P = (2a + 2b) unit

∴ P = 2(a + b) unit

∴ Perimeter of rectangle = 2(length + breadth) unit

If the length and breadth of the rectangle are a and b respectively and the perimeter is P,

P = 2(a + b) unit

## Diagonal of Rectangle

The line segment connecting two opposite vertices of a rectangle is called the diagonal of a rectangle. The length of the two diagonals are equal to each other. Each diagonal divides the rectangle into two congruent triangle.

A rectangle is showing it two equal diagonals.

And these two triangles are right triangle. Again, area of each triangle is half of the area of rectangle. Moreover, each diagonal bisects themselves.

### Diagonal of Rectangle Formula

Let a and b be the length and width respectively and d be a diagonal of a rectangle. Again, the side a and b and the diagonal d form a right triangle whose hypotenuse is d and base and height be a and b respectively. Applying Pythagorean theorem it can be written as,

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

∴ d = √(a^{2} + b^{2})

If the length is a, width is b and the diagonal is d,

d = √(a^{2} + b^{2})

### Rectangle Example

## Area of Rectangle

The product of length and breadth of a rectangle is called the area of the rectangle. The area of a rectangle means how much interior suface it contains by its four sides.

### Area of Rectangle Formula

Let the length and breadth of a rectangle a and b respectively and the area be A,

So, area of rectangle = (length × breadth) square unit

∴ A = ab square unit

If the length and breadth of a rectangle are a and b respectively and the area is A,

A = ab square unit