## Quadrilateral definition

A quadrilateral is a polygon with four sides, four vertices (corners), and four angles. It is also known as a quadrangle or tetragon. The quadrilateral is derived from two words, ‘quadri‘ which means four, and ‘lateral‘ which means side.

## Properties of Quadrilaterals:

**Sum of Interior Angles:**The sum of the interior angles of a quadrilateral is always 360 degrees.**Diagonals**: A diagonal is a line segment connecting two non-adjacent vertices of a quadrilateral. The number of diagonals in a quadrilateral is equal to half of the product of its sides minus two.**Area**: The area of a quadrilateral can be found by using different formulas based on its type.**Perimeter:**The perimeter of a quadrilateral is the sum of its four sides.

## Types of Quadrilaterals

- Parallelogram
- Rectangle
- Rhombus
- Square
- Trapezium
- Kite

Quadrilaterals can be classified into different types based on their properties and characteristics.

### 1. Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are congruent and parallel to each other. The opposite angles of a parallelogram are also congruent.

In other words a quadrilateral is a parallelogram if

- its opposite sides are equal.
- opposite angles are equal.
- its diagonals bisect each other.
- it has one pair of opposite sides parallel and equal.

### 2. Rectangle

A rectangle is a parallelogram with four right angles. The opposite sides of a rectangle are congruent and parallel to each other.

A rectangle properties are:

- opposite sides are equal.
- each angle is a right angle.
- diagonals are equal.
- diagonals bisect each other.

### 3. Rhombus

A rhombus is a parallelogram with four congruent sides. The opposite angles of a rhombus are congruent.

A rhombus properties are:

- all sides are equal.
- opposite angles are equal.
- diagonals bisect each other at a right angle.

### 4. Square

A square is a rectangle with four congruent sides. It has four right angles and is a regular quadrilateral.

A square properties are:

- all the sides are equal.
- each angle is a right angle.
- diagonals are equal.
- diagonals bisect each other at a right angle.

### 5. Trapezium

A trapezoid is a quadrilateral with at least one pair of parallel sides. The non-parallel sides are called legs and the parallel sides are called bases. A trapezium properties are:

- one pair of opposite sides is parallel.
- interior angles on the same side of each of the non-parallel sides are supplementary.

### 6. Kite

- two pairs of adjacent sides are equal and opposite sides are unequal.
- diagonals intersect each other at right angles.
- the diagonals bisects the other diagonal.
- only one pair of opposite angles is equal.

### Quadrilateral examples in real life

We can see the **shape of quadrilaterals** in several objects around us, like in a deck of cards, a chessboard, a kite, a tub of popcorn, and an arrow.

### Area of Quadrilaterals

The formula for finding the area of a quadrilateral depends on the type of quadrilateral. Here are the formulas for some common types of quadrilaterals:

Quadrilateral Type | Formula for Area |
---|---|

Square | Area = s^{2} |

Rectangle | Area = l x w |

Parallelogram | Area = b x h |

Rhombus | Area = (d_{1} x d_{2}) / 2 |

Trapezoid | Area = ((b_{1} + b_{2}) / 2) x h |

**Note:**

- “s” represents the length of a side in a square
- “l” represents the length and “w” represents the width of a rectangle
- “b” represents the length of the base and “h” represents the height of a parallelogram and trapezoid
- d
_{1}and d_{2}represent the length of the diagonals of a rhombus - In a trapezoid, b
_{1}and b_{2}represent the lengths of the parallel bases, and “h” represents the height or perpendicular distance between the bases.

## Quadrilateral Examples

**Example1: If the side length of a square is 5 cm, find the area of Square.**

Area = s^{2}

= 5^{2}

area of Square = 25 square cm

**Example2: If the length of a rectangle is 8 cm and the width is 4 cm, then find the area of Rectangle.**

Area = l x w

= 8 x 4

the area of Rectangle = 32 square cm

** Example3: If the base of a parallelogram is 10 cm and the height is 6 cm, then find the area of Parallelogram.**

Area = b x h

= 10 x 6

area of Parallelogram = 60 square cm

**Example4: If the diagonals of a rhombus are 6 cm and 8 cm, then find the area of Rhombus.**

Area = (d1 x d2) / 2

= (6 x 8) / 2

the area of Rhombus = 24 square cm

**Example5: If the two parallel bases of a trapezoid are 6 cm and 10 cm, and the height is 8 cm, then find the area Trapezoid.**

Area = ((b1 + b2) / 2) x h

= ((6 + 10) / 2) x 8

the area Trapezoid = 64 square cm